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Stoddard's  Mental  Exercises. 


TlIE 

AMERICAN 


DESIGNED     FOR    THE     USE 

OF 

SCHOOLS    AND    ACADEMIES; 

*  CONTAINING 

AN  EXTENSIVE   COLLECTION  OF  PRACTICAL  QUESTIONS,  WITH    CON 

CISE  AND  ORIGINAL  METHODS  OF  SOLUTION,  WHICH  SIMPLIFY 

MANY    OF   TI1E    MOST   IMPORTANT   RULES   IN 

WRITTEN    ARITHMETIC. 


BY  JOHN  F.  STODDARD,  A.  M., 

PRINCIPAL   OF  THE 

LANCASTER  COUNTY  NORMAL  SCHOOL, 

AUTHOR  OF 

!  JUVENILE   MENTAL,"  "  THE   1'RACTICAL,"  AND   "  THE   PHILOSOPHl 
ARITHMETICS,    "  UEAPY   RECKONER,"  ETC. 


NEW  YORK: 
SHELDON,  BLAKEMAN  &  CO. 

PHILADELPHIA,  J.  B.  LIPPINOOTT  &  CO.       I5O8TON,  JOHN  P.  JEWETT  A  CO. 

KUFKALO,  P1IIN3TEY  &  CO.    CLEVELAND,  J.  15.  COUJ5  ,fe  CO.    CINCINNATI, 

AFPLEGATE  A   CO.        DETROIT,  KERB,  MOKLEY   A   CO.        CHICAGO, 

KEENE    A     LEE.         NASHVILLE,     TOON,     NELSON     A    CO. 

BT.  LOUIS,  E.  K.   WOODWAIII)  AMI)  KEITH  &  WOODS. 


f 

•  V 


Entered  according  to  an  Act  of  Congress,  in  the  year  1849,  by 
JOHN  F.   STODDARD, 

In  the  Clerk's  Office  of  the  District  Court  of  the  United  States,  for  tit* 
Sout'ieia  District  of  New  York. 


PREFACE. 


IN  presenting  the  following  work  to  tho  public, 
I  have  been  prompted  by  no  desire  of  pecuniary 
gain,  or  wish  to  appear  in  the  capacity  of  an  au 
thor.  But  having  felt  the  necessity  of  a  more 
extended,  and  more  systematically  ammged  work 
on  the  subject,  for  the  benefit  of  younger  as  well 
as  older  and  more  advanced  pupils ; — and,  by  using 
it  in  manuscript  form,  in  my  own  school,  for  a 
number  of  years,  having  observed  the  superior 
mental  training  to  be  derived  from  its  study,  and 
the  ease  with  which  it  enabled  pupils  to  compre 
hend  the  more  advanced  branches  of  mathematics, 
I  offer  it  to  a  discriminating  public. 

While  one  object  has  been  to  produce  a  more 
profound  work  on  this  important  branch  of  study, 
than  any  with  which  I  am  acquainted ;  I  have  at 
the  same  time  exercised  much  thought  in  arrang 
ing  and  classifying  the  subjects,  so  that  they  are 
adapted  to  the  comprehension  of  very  young  pupils. 

The  rule  which  I  have  observed  in  preparing 
this  work  is,  Tell  but  ONE  thing  at  a  time,  and 
THAT  in  its  proper  place. 

It  would  be  laborious  to  point  out  all  the  par 
ticulars  in  which  this  work  differs  from  other 
similar  works;  I  shall,  therefore,  mention  those 
only  which  occur  in  giving  a  brief  exposition  of 


it  PREFACE. 

its  general  plan,  leaving  the  many  other  differ 
ences  (which,  doubtlessly,  will  be  considered  of 
much  importance)  to  be  found  by  those  who  study 
the  book. 

CHAPTERS  FIRST,  SECOND,  THIRD,  and  FOURTH, 
treat  respectively  of  Addition,  Subtraction,  Mul^ 
tiplication,  and  Division  of  simple  numbers  ;  each 
of  which  is  rendered  familiar  by  an  extensive  col 
lection  of  practical  examples.  The  last  Lesson  in 
Chapter  Second,  consists  of  practical  questions, 
which  combine  Addition  and  Subtraction.  The 
last  Lesson  in  Chapter  Third,  consists  of  practical 
questions  combining  Addition,  Subtraction  and 
Multiplication.  Thus,  an  intimate  connection  be 
tween  Lessons  and  even  Chapters  is  kept  up 
through  the  whole  work,  with  the  exception  of 
Chapter  Fifth,  which  contains  a  few  of  the  most 
important  tables  of  Weights  and  Measures  ;  each 
of  which  is  illustrated  with  appropriate  examples. 
The  table  of  Sterling  Money,  being  foreign  to  our 
currency,  has  been  omitted. 

CHAPTER  SIXTH  is  devoted  to  the  subject  of 
Fractions,  and  contains  twenty  lessons,  ia  which 
many  original  combinations  and  concise  solutions 
occur. 

CHAPTER  SEVENTH  consists  of  practical  and  in 
tricate  questions  of  various  kinds,  which  require 
for  their  solution  a  thorough  knowledge  of  the  pre 
ceding  Chapters.  This  Chapter  (the  greater  part 
of  which  is  believed  to  be  found  in  no  similar  work) 
when  thoroughly  understood,  will  be  of  incalcula 
ble  benefit  to  those  who  are  studying,  or  intend  to 
study  Algebra. 

CHAPTER  EIGHTH  includes  Interest,  Discount* 


PREFACE. 


and  per  cent,  of  every  description,  in  all  their  va 
rious  modifications.  The  method  of  treating  these 
subjects  is  original ;  and  renders  the  rules  in 
Written  Arithmetic,  under  these  heads  (which  are 
usually  so  incomprehensible  to  pupils)  perfectly  in 
telligible  by  reducing  the  whole  to  one  continued 
train  of  reasoning. 

It  is  believed  that  this  Chapter,  if  thoroughly 
taught,  cannot  fail  to  quicken,  strengthen,  and  de 
velop  the  reasoning  powers  ;  bringing  into  exer 
cise,  as  it  does,  nearly  every  principle  taught  in 
the  twenty  lessons  of  Chapter  Sixth,  and  also  the 
greater  part  of  Chapter  Seventh,  it  must  of  neces 
sity  cause  the  pupil  to  acquire  the  habit  of  syste 
matically  classifying  his  knowledge,  that  he  may, 
at  any  time,  be  able  to  call  to  his  aid,  such  por 
tions  of  it  as  will  assist  in  illustrating  or  demon 
strating  the  subject  under  consideration ; — a  habit, 
of  infinite  importance  to  a  person  in  every  condi 
tion  of  life. 

The  mind  is  composed  of  a  variety  of  faculties 
which  require  for  their  development  appropriate 
and  constant  exercise.  That  Intellectual  Arith 
metic,  properly  taught,  is  better  calculated,  than 
any  other  study,  to  invigorate  and  develop  these 
faculties,  to  produce  accurate  and  close  discrimi 
nation,  and,  to  enable  the  pupil  to  acquire  a  know 
ledge  of  the  Higher  Mathematics  with  greater  ease, 
cannot  for  a  moment  admit  of  a  doubt. 

J.  F.  STODDARD, 

LIBERTY   JAN.  1849. 


SUGGESTIONS  TO  TEACHERS 

To  those  whose  experience  is  limited,  the  Au 
thor  would  beg  leave  to  present  the  following  sug 
gestions  in  regard  to  the  most  approved  methods 
of  teaching  this  important  branch  of  study. 

First. — The  lessons  should  be  assigned  previously 
to  recitation,  to  afford  the  pupil  an  opportunity  for 
its  examination :  the  use  of  the  book,  during  class 
exercise,  should  be  entirely  prohibited. 

Secondly. — To  concentrate  the  attention  of  the 
whole  class,  questions  should  be  assigned  promis 
cuously,  and  not  in  rotation  as  is  too  frequently 
done. 

Thirdly. — No  question  should  be  read  more  than 
once,  if  done  slowly  and  distinctly  ;  the  student 
should  be  required  to  reproduce  and  solve  it  with 
out  interruption,  unless  it  be  to  make  a  necessary 
criticism  or  correction.  Care  should  be  taken 
that  the  language  of  the  pupil  be  rigidly  accurate, 
as  to  construction  and  articulation. 

Fourthly. — It  is  respectfully  suggested  that,  the 
particular  forms  given  for  the  solution  of  questions 
be  carefully  adhered  to,  unless,  better  ones  should 
be  devised  by  the  teacher, 

J.  F.  S. 


ABITHMETIC, 


CHAPTER    1 , 
LESSON    I. 

1 .  2  and  1  are  how  many  ? 

2.  2  and  2  are  how  many  ? 

3.  2  and  3  are  how  many  ? 

4.  2  and  4  are  how  many  ? 

5.  2  and  5  are  how  many  ? 

6.  2  and  6  are  how  many  ? 

7.  2  and  7  are  how  many  1 

8.  2  and  8  are  how  many  ? 

9.  2  and  9  are  how  many  ? 

10.  3  and  2  are  how  many  ? 

11.  3  and  3  are  how  many  ? 

12.  3  and  4  are  how  many  ? 

13.  3  and  5  are  how  many  if 

14.  3  and  6  are  how  many  ? 

15.  3  and  7  are  how  many  ? 

16.  3  and  8  are  how  many  ? 

17.  3  and  9  are  how  many  ? 

18.  4  and  3  are  how  many? 

19.  4  and  4  are  how  many  ? 

20.  4  und  5  are  how  many  ? 

21.  4  and  6  are  how  many  ? 

22.  4  and  7  are  how  many  ? 

23.  4  and  8  are  how  many  ? 

24.  4  and  9  are  how  many  ? 


$  ARITHMETIC. 

25.  James  killed  2  birds  and  John  1  ;  how  many 
did  they  both  kill  ? 

26.  Gave  2  cents  to  Henry,  and  2  cents  to  Harvey ; 
how  many  cents  did  they  both  receive  ? 

27.  Hiram  had  2  cents,  and  his  brother  gave  him  3 
more  ;  how  many  had  he  then  ? 

28.  George  gave  me  2  apples,  and  Mary  gave  me 
4 ;  how  many  did  they  both  give  me  ? 

29.  A  man  had  2  cows,  and  he  purchased  5  more ; 
how  many  cows  did  he  then  have  ? 

30.  John's    father   gave  him  2   oranges,   and   his 
mother  gave  him  6  ;  how  many  did  he  receive  in  all  ? 

31.  Philo  bought  2  peaches,  and  his  brother  gave 
him  7  more  ;  how  many  has  he  in  all  ? 

32.  Philip  gave  me  2  plums,  and  Myron  gave  me 
8 ;  how  many  did  they  both  give  me  ? 

33.  A  farmer  had  2  horses,  and  bought  9  more ; 
how  many  had  he  then  1 

34.  William  had  3  candies,  and  Moses  gave  him  2 
more  ;  how  many  did  he  then  have  ? 

35.  John  had  3  apples,  and  I  gave  him  3  more , 
how  many  had  he  then  ? 

36.  Philip  gave  3  cents  for  some  nvits,  and  4  cents 
for  some  candies ;  what  did  he  pay  for  both  ? 

37.  I  paid  3  cents  for  some  wafers,  and  5  cents  for 
a  stamp  ;  what  did  they  both  cost  me  ? 

38.  A  merchant  bought  3  barrels  of  sugar,  and  6 
barrels  of  molasses ;   how  many  barrels  did  he  then 
have  ? 

39.  Ralph  is  3  years  old,  and  Edward  is  7 ;  what 
is  the  sum  of  their  ages  ? 

40.  A  lemon  cost  3  cents,  and  a  pine-apple  cost  8 ; 
what  was  the  cost  of  both  ? 

41.  James  solved  3  questions  in  arithmetic,   and 
Oliver  9 ;  how  many  did  they  both  solve  ? 

12.  If  it  take  4  yards  of  cloth  for  a  coat,  and  3  for 
•  pair  of  pams,  how  many  yards  will  it  take  for  both  ? 


ARITHMETIC.  9 

43.  Samuel  had  4  marbles,  and  found  4   more  ; 
how  many  had  he  then  ? 

44.  Isaac  bought  4  sheets  of  paper,  and  I  gave  him 
5  more ;  how  many  had  he  then  ? 

45.  If  a  peck  of  apples  cost  4  cents,  and  a  peck  of 
pears  6  cents,  what  is  the  cost  of  the  apples  and  pear 
together  ?  \ 

46.  If  Mary  has  4  books,   and  her  father  should 
give  her  7  more,  how  many  would  she  then  have  ? 

47.  William  has  4  marbles  in  his  hand,  and  8  in 
his  pocket ;  how  many  has  he  in  all  ? 

48.  Charles  walked  4  miles,  and  rode  9 ;  how  far 
did  he  go  ? 

49.  In  a  certain  class  there  are  5  boys,  and  4  girls ; 
how  many  scholars  are  there  in  the  class '/ 

50.  Jacob  bought  6  apples,  and  Jeremiah  bought 
7 ;  how  many  did  they  both  buy  ? 


LESSON     .[. 

1 .  5  and  4  are  how  many  ? 

2.  5  and  5  are  how  many  ? 

3.  5  and  6  are  how  many 

4.  5  and  7  are  how  many  ? 

5.  5  and  8  are  how  many  ? 

6.  5  and  9  are  how  many  ? 

7.  6  and  5  are  how  many  ? 

8.  6  and  6  are  how  many  ? 

9.  6  and  7  are  how  many  ? 

10.  6  and  8  are  how  many  'i 

11.  6  and  9  are  how  many  ? 

12.  7  and  6  are  how  many  *- 

13.  7  and  7  are  how  many  ? 

14.  7  and  8  are  how  maaj  ? 

15.  7  and  9  are  how  many  t 


10  ARITHMETIC. 

16.  8  and  7  are  how  many  ? 

17.  8  and  8  are  how  many  ? 

18.  8  and  9  are  how  many  ? 

19.  8  and  5  are  how  many  ? 

20.  9  and  6  are  how  many  ? 

21.  9  and  8  are  how  many  ? 

22.  9  and  9  are  how  many  ? 

23.  9  and  10  are  how'many  ? 

24.  9  and  7  are  how  many  ? 

25.  9  and  11  are  how  many? 

26.  Mary  has  answered  5  questions  correctly  and 
i  incorrectly  ;  how  many  questions  was  she  asked  ? 

27.  A  beggar  met  two  boys  ;  one  gave  him  5  cents, 
and  the  other  gave  him  6  cents ;  how  many  cents  did 
they  together  give  him  ? 

28.  A  man  bought  a  hat  for  5  dollars,  and  a  pair 
of  boots  for  6  dollars  ;  what  was  the  cost  of  both  ? 

29.  There  are  9  boys  on  one  bench,  and  8  on  an 
other  ;  how  many  are  there  on  both  ? 

30.  Maria  gave  her  teacher  5  pinks  and  7  roses ; 
how  many  flowers  did  she  give  him  ? 

31.  Harry  caught  5  squirrels,  and  Henry  caught 
8  ;  how  many  did  they  both  catch  ? 

32.  If  we  learn  5  pages  this  week,  and  9  next ; 
how  many  will  we  learn  in  two  weeks  ? 

33.  Frank  sold  a  melon  for  6  cents,  and  an  orange 
for  5  cents ;  how  many  cents  did  he  receive  for  both  ? 

34.  John  had  6  whips,   and    Joseph  gave  him  6 
more ;  how  many  had  he  then  ? 

35.  George  had  6  chestnuts,  and  Richard  gave  him 
7  more ;  how  many  had  he  then  ? 

36.  Henry  bought  6  candies,  and  Sarah  bought  8 ; 
how  many  were  bought  by  both  ? 

37.  Rebecca  has  6  oranges,  and  Catherine  has  9; 
how  many  oranges  have  Rebecca  and  Catherine  ? 

38.  A  boy  had  7  apples,  and  his  father  gave  him  0 
more ;  how  many  had  he  then  ? 


ARITHMETIC.  11 

39.  Minerva  had  7  yards  of  ribbon,  and  her  mother 
gave  her  7  more  ;  how  many  yards  did  she  then  have  ? 

40.  7  boys  were  sitting  on  one  bench,  and  8  on 
another ;  how  many  were  there  on  both  ? 

41.  7  boys  were  at  play,  and  9  other  boys  joined 
hem  ;  how  many  were  there  in  all  ? 

42.  If  I  have  8  cents  in  one  hand,  and  7  cents  in 
the  other,  how  many  have  I  in  both  ? 

43.  If  Mary  has  8  peaches,  and  Margaret  has  9, 
how  many  have  they  both  ? 

44.  Sally  gave  9  cents  for  some  thread,  and  7  cents 
for  some  needles ;   how  much  did  the  needles  and 
thread  cost  her  ? 

45.  Charles  has  9  marbles,  and  Albert  has  5 ;  how 
many  marbles  have  Charles  and  Albert  ? 

46.  9  birds  were  in  a  tree,  and  6  were  on  the 
ground  ;  how  many  were  there  in  all  ? 

47.  Sarah  gave  9  cents  for  some  cinnamon,  and  7 
cents  for  some  raisins ;  how  many  cents  did  they  cost 
her? 

48.  George  shot  9  pigeons,  and  James  shot  8 ;  how 
many  did  they  both  shoot  ? 

49.  Russel  caught  7   fish,  and  Robert  caught  5 ; 
how  many  did  they  both  catch  ? 

50.  In  one  field  there  are  8  horses,  and  in  anothei 
there  are  9 ;  how  many  are  there  in  both  ? 


LESSON     111. 

1.  How  many  are  10  and  2  ?  10  and  3  ?  10  and  4  ? 
10  and  5  ?  10  and  6  ?  10  and  7  ?  10  and  9  ?  10  and  8  ? 
10  and  10? 

2.  How  many  are  2  and  2  ?  2  and  12  ?  2  and  22  ? 
2  and  32  ?  2  and  42  ?  2  and  52  ?  2  and  62  ?  2  and 
72  ?  2  and  82  ?  2  and  92  ? 


12  ARITHMETIC. 

3.  How  many  are  3  and  3  ?  3  and  13  ?  3  and  23  I 
3  and  33  ?  3  and  43  ?  3  and  53  ?  3  and  63  ?  3  and  73  ? 

3  and  83  ?  3  and  93  ?  96  and  4  ? 

4.  How  many  are  4  and  4  ?  4  and  14  ?  4  and  24  ? 

4  and  34  ?  4  and  44  ?  4  and  54  ?  4  and  64  ?  4  and  74  ? 

4  and  84  ?  4  and  94  ?  98  and  2  ? 

5.  How  many  are  5  and  5  1  5  and  15  ?  5  and  25  ? 

5  and  35  ?  5  and  45  ?  5  and  55  ?  5  and  65  ?  5  and  75  ? 

5  and  85  ?  5  and  95  ? 

6.  How  many  are  6  and  6  ?  6  and  16  ?  6  and  26  ? 

6  and  36  ?  6  and  46  ?  6  and  56  ?  6  and  66  ?  6  and  76  ? 

6  and  86  ?  6  and  96  ? 

7.  How  many  are  7  and  7  ?  7  and  17  ?  7  and  27  ? 

7  and  87  ?  7  and  47  ?  7  and  57  1  7  and  67  ?  7  and  77  ? 

7  and  87  ?  7  and  97  I 

8.  How  many  are  8  and  8  ?  8  and  18  ?  8  and  28  ? 

8  and  38  ?  8  and  48  ?  8  and  58  ?  8  and  68  ?  8  and  78  ? 

8  and  88  ?  8  and  98  ? 

9.  How  many  are  9  and  9  ?  9  and  19  ?  9  and  29  ? 

9  and  39  ?  9  and  49  ?  9  and  59  ?  9  and  69  ?  9  and  79  ? 

9  and  89  ?  9  and  99  ? 

10.  How  many  are  10  and  11  ?  10  and  21  ?  10  and 

31  ?  10  and  41  ?  10  and  51  ?  10  and  61  ?  10  and  71  ? 

10  and  81  ?  10  and  91  ? 

11.  How  many  are  10  and  12  ?  10  and  22  ?  10  and 

32  ?  10  and  42  ?  10  and  52  ?  10  and  62  ?  10  and  72  ? 
10  and  82  1  10  and  92  ? 

12.  How  many  are  10  and  4  ?  10  and  14  ?  10  and 
24  ?  10  and  34  ?  10  and  44  ?  10  and  54  ?  10  and  64  ? 

10  and  74  ?  10  and  84  ?  10  and  94  ? 

13.  How  many  are  11  and  3  ?  11  and  13  ?  11  and 

23  I  11  and  33  ?  11  and  43  ?  11  and  53  ?  11  and  63? 

11  and  73  ?  11  and  83  ?  11  and  93  ? 

14.  How  many  are  11  and  4?  11  and  14?  11  and 

24  ?  11  and  34  I  11  and  44  ?  11  and  54  ?  11  and  64  ? 
11  and  74  1  11  and  84  ?  11  and  94  ? 

15.  How  many  are  10  and  5  ?  10  and  15  ?  10  and 


ARITHMETIC.  13 

35  ?  10  and  45  ?  10  and  55  ?  10  and  65  ?  10  and  75  ? 

10  and  85  ?  10  and  95  ?  10  and  25  ? 

16.  How  many  are  11  and  5?  11  and  15?  11  and 
25  ?  11  and  35  ?  11  and  45  ?  11  and  55  ?  11  and  65  ? 

11  and  75  ?  11  and  85?  11  and  95? 

17.  How  many  are  3  and  8  ?  3  and  18  ?  3  and  28? 
3  and  38  ?  3  and  48  ?  3  and  58  ?  3  and  68  ?  3  and  78? 
3  and  88?  3  and  98? 

18.  How  many  are  8  and  4  ?  8  and  14  ?  8  and  24  ? 
8  and  34  ?  8  and  44  ?  8  and  54  ?  8  and  64  ?  8  and  74  ? 
8  and  84  ?  8  and  94  ? 

19.  How  many  are  7  and  5  ?  7  and  17  ?  7  and  27  ? 
7  and  37  ?  7  and  47  ?  7  and  57  ?  7  and  67  ?  7  and  77  ? 

7  and  87  ?  7  and  97  ? 

20.  How  many  are  8  and  6  ?  8  and  16  ?  8  and  26  ? 

8  and  36  ?  8  and  46  ?  8  and  56  ?  8  and  66  ?  8  and  76  ? 
8  and  86  ?  8  and  96  ? 


LESSON    IV, 

1.  8  and  9  are  how  many? 

2.  11  and  7  are  how  many? 

3.  10  and  9  are  how  many? 

4.  7  and  14  are  how  many  ? 

5.  6  and  12  are  how  many  ? 

6.  9  and  15  are  how  many  ? 

7.  11  and  18  are  how  many  ? 

8.  15  and  12  are  how  many  ? 

9.  14  and  13  are  how  many? 

10.  16  and  14  are  how  many  ? 

11.  21  and  12  uve  how  many  ? 

12.  24  and  13  are  how  many? 

13.  25  and  15  are  how  many  p 

14.  27  and  13  are  how  many? 

15.  23  and  17  are  how  many  ? 


'4  ARITHMETIC. 

16.  29  and  11  are  how  many? 

17.  80  and  20  are  how  many  ? 

18.  34  and  15  are  how  many  ? 

19.  32  and  18  are  how  many  ? 

RKMARX.— The  symbol  -H,  is  called  plus;  and  denotes  that  the  quantt 
es  between  which  it  is  placed,  are  to  be  added  Thus  4  «f  3  shews  thai 
and  -2  are  to  be  added  ; — and  is  read,  four  plus  two. 

20.  33  +  44  are  how  many  ? 

21.  35  -|-  15  are  how  many  '£ 

22.  36  +  12  are  how  many  1 

23.  40  +  36  are  how  many  ? 

24.  40  -f-  29  are  how  many  ? 

25.  44  +  20  are  how  many  ? 

26.  48  +  32  are  how  many  ? 

27.  45  +  35  are  how  many  ? 

28.  4  +  8  +  6  are  how  many  ? 

29.  8  +  2  +  7  are  how  many  ? 

30.  10  +  7  +  3  are  how  many  ? 

31.  12  +  10  +  9  are  how  many  ? 

32.  15  +  12  +  6  are  how  many  ? 

33.  18  +  4  +  10  are  how  many  ? 

34.  24  +  16  +  12  are  how  many  ? 

35.  22  +  33  +  11  are  how  many  ? 

36.  15  +  16  +  2  are  how  many  ? 

37.  28  +  12  +  15  are  how  many  ? 

38.  46  +  24  +  19  are  how  many  ? 

39.  12  +  8  +  6  +  4  are  how  many  ? 

40.  24  +  10  +  6  +  12  are  how  many  I 


LESSON    V. 

1.  Three  boys,  James,  Joseph  and  Jacob,  gave  some 
money  to  a  beggar ;  James  gave  him  6,  Joseph  8,  and 
Jacob  10  cents ;  how  many  cents  did  they  all  give 
him? 


ARITHMETIC.  15 

2.  Gave  8  cents  to  John,  4  cents  to  Morgan  and  2 
cents  to  Samuel ;   how  many  cents  did  they  all  re 
ceive  ? 

3.  Henry  has  3  marbles,  Harvey  has  10,  and  Harry 
lias  7  ;  how  many  marbles  have  they  all  ? 

4.  Gave  7  nuts  to  one  boy,  6  to  another,  and  7  to 
another ;  how  many  nuts  did  the  three  boys  receive  ? 

5.  Bought  a  basket  of  strawberries  for  7  cents,  a 
basket  of  cherries  for  4  cents,  and  a  basket  of  plums 
for  8  cents ;  what  did  they  all  cost  ? 

6.  Lydia  has  9  pinks,  Mary  10,  and  Ann  7 ;  how 
many  pinks  have  they  all  ? 

7.  Bought  a  knife  for  14  cents,  and  a  ball  for  12 
cents  ;  what  did  they  both  cost  ? 

8.  Gave  18  cents  for  an  arithmetic,  2  for  a  pencil, 
and  10  for  a  slate ;  what  did  they  all  cost  ? 

9.  James  had  12  cents,  and  his  mother  gave  him  13 
more ;  how  many  had  he  then  ? 

10.  Robert  shot  9  birds,  Richard  shot  11,  and  James 
shot  12  ;  how  many  did  they  all  shoot  ? 

11.  A  boy  bought  a  pound  of  butter  for  14  cents,  a 
pound  of  meat  for  8  cents,  and  a  bunch  of  lettuce  for 
7  cents ;  what  was  the  whole  cost  ? 

12.  Bought  a  pound  of  raisins  for  10  cents,  a  pound 
of  candies  for  12  cents,  and  a  pound  of  cinnamon  for 
15  cents  ;  what  was  the  whole  cost  ? 

13.  John  had  20  marbles,  Matthew  9,  and  Morgan 
12 ;  how  many  did  they  all  have  ? 

14.  James  bought  a  pigeon  for  9  cents,  a  robin  for 
10  cents,  and  a  squirrel  for  12  cents ;  what  did  they 
all  cost  him  ? 

15.  A  lady  bought  some  pins  for  15  cents,  some 
thread  for  10  cents,  and  some  lace  for  18  cents ;  what 
did  all  these  articles  cost  her  ? 

16.  A  gentleman  bought  a  hat  for  6  dollars,  a  vest 
for  5  dollars,  and  a  coat  for  20  dollars ;  what  did  he 
pay  for  them  all  ? 


18  ARITHMETIC. 

17.  A  man  bought  a  watch  for  40  dollars,  a  gold 
chain  for  15  dollars,  and  a  gold  pen  for  5  dollars ; 
what  did  he  pay  for  these  three  articles? 

18.  Jackson  gave  25  cents  to  his  sister,  and  23 
cents  to  his  mother ;  how  many  cents  did  he  give 
away  ? 

19.  Bought  a  barrel  of  flour  for  7  dollars,  a  barrel 
•>f  pork  for  12  dollars,  and  a  barrel  of  fish  for  11  dol 
lars  ;  what  was  the  whole  cost  ? 

20.  Bought  a  horse  for  60  dollars,  a  cow  for  20 
dollars,  and  a  colt  for  25  dollars :   what  did  they  all 
cost? 

21.  If  your  father  should  give  you  12  cents,  your 
mother  14  cents,  and  your  sister  4  cents ;   how  many 
cents  would  you  then  have  ? 

22.  A  boy  spent  11  cents  for  confectionary,  9  centd 
for  a  ball,  and  5  cents  for  a  to/; ;  what  did  th^r  all 
cost  him  ? 

23.  A  man  bought  some  butter  for  57  dollars,  and 
some  molasses  for  23  dollars ;  what  was  the  cost  of 
both? 

24.  A  boy  travelled  17  miles  one  day,  and  23  the 
next ;  how  far  did  he  travel  in  the  two  days  ? 

25.  A  lady  bought  a  hat  for  7  dollars,  a  dress  for  9 
dollars,  and  a  gold  watch  for  60  dollars ;   what  was 
the  whole  cost  ? 

26.  A  mechanic  sold  a  wagon  for  57  dollars,  and  a 
sleigh  for  43  dollars  ;  what  did  he  receive  for  both  ? 

27.  A  boy  saw  24  pigeons  on  one  tree,  and  36  on 
another ;  how  many  did  he  see  in  all  ? 

28.  In  a  certain  recitation  21  questions  were  an 
swered  correctly,  and  9  incorrectly  ;  how  many  ques 
tions  were  asked  during  the  recitation  ? 

29.  Gave  87  dollars  for  a  chaise,  2  dollars  for  * 
whip,  and  11  dollars  for  a  Buffalo- robe ;  what  was  the 
whole  cost  ? 


ARITHMETIC.  17 

30.  If  a  horse  is  worth  60  dollars,  and  a  sleigh  75 
dollars,  what  is  the  value  of  both  ? 

31.  Matthew  is  15  years  old,   Morgan  is  7,  and 
Martin  is  10;  what  is  the  sum  of  their  ages? 

32.  A  man  bought  a  load  of  hay  for  7  dollars,  a 
load  of  rye  for  36  dollars,  and  a  load  of  wheat  for  17 
dollars ;  what  was  the  whole  cost  ? 

33.  A  man  is  48  years  old,  and  his  wife  is  32  years 
old  ;  what  is  the  sum  of  their  ages  ? 

34.  A  farmer  bought  a  horse  for  60  dollars,  and  a 
yoke  of  oxen  for  75  dollars ;  what  did  the  horse  and 
oxen  cost  him  1 

35.  John  gave  11  candies  to  his  brother,  9  to  his 
sister,  and  kept  12  himself;   how  many  had  he  at 
first? 

36.  Simeon  hoed  12  rows  of  corn,  Simon  15,  James 
13,  and  John  11  ;   how  many  rows  did  they  together 
hoe? 

37.  A  merchant  sold  30  barrels  of  flour  one  week, 
37  the  next  week,  and  33  the  following  week ;  how 
many  barrels  did  he  sell  during  the  three  weeks  ? 

38.  A  merchant  sold  a  barrel  of  sugar  for  5  dollars, 
a  barrel  of  rum  for  15  dollars,  and  a  hogshead  of  mo 
lasses  for  23  dollars ;  what  did  he  receive  for  all  these 
articles  ? 

39.  A  man  bought  a  firkin  of  butter  for  9  dollars, 
a  keg  of  molasses  for  7  dollars,  a  box  of  cheese  for  4 
dollars,  and  a  box  of  faisins  for  5  dollars ;  what  was 
the  whole  cost  ? 

40.  A  lady  bought  a  silk  dress  for  18  dollars,  a 
muff  for  12  dollars,  a  shawl  for  17  dollars,  and  a  pair 
of  gloves  for  1  dollar :  the  whole  cost  is  required. 


18  ARITHMETIC. 

CHAPTER    II. 
LESSON    I. 

1.  If  I  have  3  apples,  and  give  1  of  them  to  Rich 
ard,  how  many  shall  I  have  left  ? 

SOLUTION.— If  I  have  3  apples  and  give  1  of  them  away,  there  will  b* 
remaining  the  difference  between  3  and  1  which  is  2.  Therefore  I  have 
3  left. 

2.  William  had  4  chestnuts,  and  gave  1  to  his  broth- 
er ;  how  many  had  he  left  ? 

3.  Martha  had  5  books,  and  on  her  way  to  school 
rihe  lost  1  of  them ;  how  many  had  she  left  ? 

4.  Cornelia  had  6  apples  and  gave  1  to  her  brother ; 
how  many  had  she  left  ? 

5.  Rachel  had  10  pins  and  lost  1   of  them ;   how 
many  had  she  left  ? 

6.  Martha  had  12  pears  and  gave  2  to  Elizabeth ; 
how  many  had  she  left  ? 

7.  If  you  had  5  candies  and  should  give  2  of  them 
away,  how  many  would  you  have  left  ? 

8.  James  had  6  apples  and  gave  2  away;    how 
many  had  he  remaining  ? 

9.  Cornelia  says  she  has  learned  12  letters  to-day, 
but  has  forgotten  3  of  them ;  how  many  does  she  re 
member  ? 

10.  James  had  10  marbles  and  lost  3 ;  how  many 
had  he  left? 

11.  Mary  found  9  roses  on  her  bush,  and  picked 
off  4  of  them ;  how  many  remained  on  the  bush  ? 

12.  4  less  2  are  how  many  ? 

13.  5  less  3  are  how  many  ? 

14.  7  less  3  are  how  many  ? 

15.  9  less  4  are  how  many  ? 

16.  9  less  3  are  how  many  ? 


ARITHMETIC.  19 

17.  9  less  7  are  how  many  ? 

18.  9  less  5  are  how  many  ? 

19.  11  less  4  are  how  many  ? 

20.  10  less  4  are  how  many  ? 

21.  11  less  5  are  how  many? 

22.  14  less  4  are  how  many  ? 

23.  8  less  5  are  how  many  ? 

24.  13  less  3  are  how  many  ? 

25.  14  less  5  are  how  many  ? 

26.  17  less  7  are  how  many  ? 

27.  15  less  5  are  how  many  ? 

28.  13  less  10  are  how  many  ? 

29.  23  less  3  are  how  many  ? 

30.  27  less  7  are  how  many  ? 

REMARK.— -The  symbol  — ,  is  called  minus ;  and  denotes  that  the  quantity 
>n  the  right  of  it  is  to  be  taken  from  the  quantity  on  the  left.  Thus,  6  —  4 
jhows  that  4  is  to  be  subtracted  from  6  ; — and  is  read,  six  minus  four. 

The  symbol  =,  means  equal  to,  and  when  placed  between  two  quaatitr^j 
It  denotes  that  they  are  equal  to  each  other.  Thus,  4  -f-  2  =  6,  is  rea-i  4 
plus  2,  or  4  added  to  2  is  equal  to  6. 

31.  8  —  5  are  how  many? 

32.  9  —  7  are  how  many  ? 

33.  10  —  8  are  how  many? 

34.  11— -8  are  how  many  ? 

35.  12  —  6  are  how  many? 

36.  13  —  8  are  how  many  ? 

37.  14  —  8  are  how  many  ? 

38.  18  —  8  are  how  many? 

39.  22 —  12  are  how  many  ? 

40.  24  — 14  are  how  many  ? 

41.  12  —  4  are  how  many  ? 

42.  28  —  8  are  how  many  ? 

43.  20  —  5  are  how  many  ? 

44.  20  —  8  are  how  many  ? 

45.  20  —  9  are  how  many  ? 

46.  20  —  7  are  how  many  ? 

47.  20  — 10  are  how  many  I 

48.  20  — 15  are  how  many  I 

49.  24  — 10  are  how  many  f 


20  ARITHMETIC. 

50.  25  — 10  are  how  many  ? 

51.  26  — 10  are  how  many  ? 

52.  28  — 10  are  how  many  ? 

53.  27  —  10  are  how  many  ? 

54.  29  — 10  are  how  many  ? 

55.  32  — 10  are  how  many? 

56.  34  — 10  are  how  many  1 

57.  36  —  10  are  how  many  ? 

58.  35  —  10  are  how  many  ? 

59.  37  — 10  are  how  many  ? 

60.  38  — 10  are  how  many  ? 

61.  39  — 10  are  how  many  ? 

62.  47  — 10  are  how  many  ? 

63.  40  — 12  are  how  many  ? 

64.  42  —  20  are  how  many  ? 

65.  45  —  20  are  how  many  ? 

66.  46  —  20  are  how  many  ? 

67.  47  —  20  are  how  many  ? 

68.  47  —  37  are  how  many  ? 

69.  49  — 19  are  how  many  ? 

70.  52  —  22  are  how  many? 

71.  54  —  34  are  how  many  ? 

72.  56  —  46  are  how  many  ? 

73.  57  —  27  are  how  many? 

74.  58  —  48  are  how  many  ? 

75.  62  —  30  are  how  many? 

76.  65 — 40  are  how  many? 

77.  68  —  48  are  how  many  ? 

78.  74  —  34  are  how  many  ? 

79.  Gave  7  cents  for  a  spool  of  thread,  and  4  ccntt 
for  a  lemon ;  how  much  more  did  the  thread  cost  than 
the  lemon  ? 

80.  Paid  18  cents  for  a  pound  of  butter,  and  8  cents 
for  a  pound  of  meat ;  how  much  more  was  paid  for  the 
butter  than  for  the  meat  ? 

81.  James  bought  18  candies,  and  gave  John  7  of 
them  ;  how  many  had  he  left  ? 


ARTTIIMETIC.  21 

82.  Sold  a  quantity  of  wool  for  27  dollars,  and  re 
ceived  in  payment  a  barrel  of  flour  worth  5  dollars*, 
how  many  dollars  remain  due  ? 

83.  James  has  27  marbles,  and  John  has  17  ;  how 
many  more  has  James  than  John  ? 

84.  Harry  is  15  years  old,  and  Henry  is  9  year* 
old ;  how  many  years  older  is  Harry  than  Henry  ? 

85.  A  teacher  being  asked  how  many  scholars  he 
had,  answered  that  he  usually  had  37,  but  at  present 
he  had  only  27 ;  how  many  were  absent  ? 

86.  A  man  purchased  a  watch  for  37  dollars,  but 
found  he  had  only  24  dollars  with  him ;   how  much 
must  he  borrow  in  order  to  pay  the  balance  ? 

87.  Mr.   A   has    94  sheep,   and    B   has   44 ;   how 
many  more  sheep  has  A  than  B  ? 

88.  Morgan  gave  23  cents  for  some  cake,  and   14 
cents  for  some  cinnamon ;   how  much  more  did  the 
cake  cost  than  the  cinnamon  ? 

89.  Michael  had  29  cents  and  lost  14;   how  many 
had  he  left? 

90.  In  a  certain  recitation  47  questions  were  asked, 
and  9  of  them  were  answered  incorrectly ;  how  many 
were  correctly  answered  ? 

91.  A  man  sold  23  sheep  from  a  flock  consisting 
of  93  ;  how  many  sheep  remained  ? 

92.  Mr.  B   bought  a  horse  for  35  dollars,  and  sold 
it  for  46  dollars ;  how  much  did  he  gain  ? 

93.  A  cow  was  bought  for  25  dollars  and  sold  for 
19  dollars ;  how  much  was  the  loss  ? 

94.  A  merchant  bought  a  quantity  of  goods  for  95 
d  )llars,  but  being  damaged  was  obliged  to  sell  them 
for  80  dollars ;  how  much  did  he  lose  ? 

95.  From  a  vessel  containing  57  gallons,  27  gallons 
leaKed  out ;  how  much  remained  in  ? 

96.  A  merchant  bought  a  quantity  of  silk  for  47 
dollars,  and  sold  it  for  67   dollars ;  how  much  did  he 
gain  by  the  bargain  ? 


22  ARITHMETIC. 

97.  A  butcher  has  57  sheep  and  44  lambs ;  how 
many  more  sheep  has  he  than  lambs  ? 

98.  Paid  97  dollars  for  a  quantity  of  sugar,  and  48 
dollars  for  some  molasses ;   how  much  more  did  the 

ugar  cost  than  the  molasses  ? 


LESSON    II. 


1.  A  boy  has  7  chestnuts  in  one  hand,  and  4  in  thft 
other ;  how  many  more  has  he  in  one  hand  than  in  the 
other,  and  how  many  in  both  ? 

2.  Bought  a  barrel  of  fish  for  8  dollars,  and  some 
quinces  for  3  dollars  ;   how  much  more  did  the  fish 
cost  than  the  quinces  ?     What  was  the  cost  of  both  1 

3.  Gave  15  dollars  for  a  cow  and  6  dollars  for  a 
sheep ;  how  much  more  was  given  for  the  cow  than 
for  the  sheep  ?     What  was  given  for  both  ? 

4.  Phineas  gave  50  cents  for  a  grammar,  and  25 
cents  for  an  arithmetic  ;  what  was  the  cost  of  both  ? 
How  much  did  one  cost  more  than  the  other  ? 

5.  Paid  15  dollars  for  a  barrel  of  rum,  and  6  dollars 
for  a  barrel  of  flour ;  what  was  the  cost  of  both  ;  and 
how  much  more  did  the  rum  cost  than  the  flour  ? 

6.  Sold  a  firkin  of  butter  for  10  dollars,  a  keg  of 
cheese  for  5  dollars,  and  received  in  payment  a  barrel 
of  flour  worth  6  dollars ;  how  much  remains  due  ? 

7.  James  gave  12  cents  for  oranges,  15  cents  for 
cake,  and  had  13  cents  remaining ;  how  much  had  he 
at  first  ? 

8.  Mary  bought  a  comb  for  10  cents,  a  spool  ot 
thread  for  12  cents,  and  a  paper  of  needles  for  8 
cents ; — she  handed  the  clerk  37  cents ;   how  much 
change  ought  she  to  receive  ? 


ARITHMETIC.  23 

9.  A  man  sold  a  cow  for  20  dollars,  a  calf  for  4 
dollars,  and  a  sheep  for  3  dollars ;  and  in  payment  re- 
ceived  a  wagon  worth  17  dollars ; — how  much  remains 
due? 

10.  A  lady  bought  a  ribbon  for  24  cents,  some  tape 
for  8  cents,  and  some  thread  for  12  cents, — she  had 
only  60  cents ;  how  much  remained  after  she  paid  for 
these  articles  ? 

11.  Stephen,  at  a  game  of  marbles,  won  4  and  lost 
6,  and  then  had  only  8  remaining;  how  many  had  he 
at  first  ? 

12.  Sampson  having  9  apples,  gave  4  to  his  mother 
and  3  to  his  sister ; — for  his  generosity  his  father  gave 
him  13  more ;  how  many  had  he  then  ? 

13.  A  man  bought  some  cloth  for  12  dollars,  and 
sold  it  for  18  dollars  ;  what  was  his  gain  ? 

14.  A  farmer  bought  a  horse  for  63  dollars    *nd 
exchanged  it  for  a  yoke  of  oxen, — these  he  so1    4or  8" 
dollars ;  what  did  he  gain  by  the  operatior  .- 

15.  A  man  bought  a  yoke  of  oxen   for  97  dollars, 
their  services  amounted  to  40  dollars,  and  their  keep 
ing  to  13  dollars, — he  then  sold  them  for  80  dollars; 
did  he  gain  or  lose,  and  how  much  ? 

16.  A  box  of  raisins  was  bought  for   3  dollars,  a 
firkin  of  butter  for  15  dollars,  and  were  both  sold  for 
20  dollars ;  how  much  was  gained  ? 

17.  A  farmer  sold  a  cow  for  29  dollars,  which  was 
6  dollars  more  than  she  cost ;  what  did  she  cost  ? 

18.  A  drover  bought  some  sheep  for  40  dollars, 
some  cattle  for  130  dollars,  and  sold  them  all  for  200 
dollars  ;  what  was  his  gain  ? 

19.  A  jeweler  bought  a  watch   for  20  dollars,  a 
chain  for  10  dollars,  a  key  for  2  dollars,  and  sold  them 
all  for  42  dollars ;  how  much  did  he  gain  by  the  bar- 
gain? 

20.  24  +  12  -f  9  are  how  many? 

21.  10  +  30  -f  15  are  how  many  ? 


24  ARITHMETIC. 

22.  14  +  16  +  11  are  how  many  ? 

23.  36   f-  9— -12  are  how  many? 

24.  38  f  22  —  15  are  how  many  ? 

25.  43  +  37  —  20  are  how  many  ? 

26.  13  +  26  —  25  are  how  many  ? 

27.  44  —  22  +  10  —  12  are  how  many  ? 

28.  27  +  23  —  20  +  2  are  how  many  ? 

29.  15  +  25  —  30  +  15  are  how  many  ? 

30.  20  +  40  —  30  +  10  are  how  many  ? 

31.  A  boy  bought  a  ball  for  6  cents ;  for  what  mu? 
he  sell  it  to  gain  4  cents  ? 

32.  A  merchant  bought  a  hogshead  of  molasses  for 
47  dollars,  and  paid  3  dollars  for  cartage ;    for  what 
must  he  sell  it  to  gain  12  dollars? 

33.  A  grocer  bought  a  hogshead  of  sugar  for  30 
dollars  ;  for  what  must  he  sell  it  to  gain  18  dollars 
by  ..   *  bargain  ? 

34.  ^  drover  bought  sheep  as  follows :  of  one  man 
he  boughi   44,  of  another  8,  and  of  another  22, — he 
then  sold  20  of  them ;  how  many  remained  unsold  ? 

35.  A  watch  cost  40  dollars ;  how  must  it  be  sold 
to  gain  13  dollars? 

36.  Four  boys  bought  a  melon ;  one  gave  3  cents, 
another  4,  another  8>  and  the  other  6  ;  what  did  the 
melon  cost  ? 

37.  Mary  bought  16  candies  at  one  shop,  and  13  at 
another, — on  her  way  home  she  ate  1 1  of  them ;  how 
many  had  she  left  ? 

38.  Matthew  had  9  nuis,  Mary  gave  him  10  more, 
and  John  gave  him  enough  to  make  his  number  39  ,* 
how  many  did  John  give  him  ? 

39.  A  farmer  had  25  sheep  in  one  field  and  15  in 
another, — he  then  bought  enough  to  make  his  number 
56 ;  how  many  did  he  buy  ? 

40.  John  has  34  marbles,  and  Albert  25;  how  many 
have  they  botli ;  and  how  many  more  has  the  one  than 
the  other  1 


AHITHMETIC.  25 

CHAPTER    III. 
LESSON    I. 

1.  Two  times  1  are  how  many  ? 

2.  Two  times  2  are  how  many  ? 

3.  Two  times  3  are  how  many  ? 

4.  Two  times  4  are  how  many  ? 

5.  Two  times  5  are  how  many  ? 

6.  Two  times  6  are  how  many  ? 

7.  Two  times  7  are  how  many  ? 

8.  Two  times  8  are  how  many  ? 
0.  Two  times  9  are  how  many  ? 

10.  Two  times  10  are  how  many  ? 

11.  Two  times  11  are  how  many  ? 

12.  Two  times  12  are  how  many  ? 

13.  What  cost  2  oranges,  at  3  cents  a  piece  ? 

SOLUTION. — If  1  orange  cost  3  cents,  2  oranges  will  cost  two  times  8 
ctnrils  5  winch  are  6  cents. 

14.  What  cost  2  peaches,  at  2  cents  a  piece  ? 

15.  What  cost  2  apples,  at  3  cents  a  piece  ? 

16.  What  cost  2  pine-apples,  at  8  cents  a  piece  ? 

17.  What   cost   2   pounds  of  meat,  at  5  cents  a 
pound  ? 

18.  What  cost  2  pounds  of  cinnamon,  at  11  cents  a 
pound  ? 

19.  What  cost  2  pounds  of  raisins,  at  12  cents  a 
pound? 

20.  What  cost  2  citrons,  at  10  cents  a  piece  ? 

21.  What  cost  2  quarts  of  cherries,  at  9  cents  a 
quart? 

22.  What  cost  2  lemons,  at  4  cents  a  piece  ? 

23.  Three  times  2  are  how  many  ? 

24.  Three  times  3  are  how  many  ? 

25.  Three  times  4  are  how  many  ? 


38  ARITHMETIC. 

26.  Three  times  5  are  how  many  ? 

27.  Three  times  6  are  how  many  ? 

28.  Three  times  7  are  how  many  ? 

29.  Three  times  8  are  how  many  ? 

30.  Three  times  9  are  how  many  ? 

31.  Three  times  10  are  how  many  ? 

32.  Three  times  11  are  how  many  ? 

33.  Three  times  12  are  how  many  ? 

34.  Four  times  3  are  how  many  ? 

35.  Four  times  4  are  how  many  ? 

36.  Four  times  5  are  how  many  ? 

37.  Four  times  6  are  how  many  ? 

38.  Four  times  7  are  how  many  ? 

39.  Four  times  8  are  how  many  ? 

40.  Four  times  9  are  how  many  ? 

41.  Four  times  10  are  how  many  ? 

42.  Four  tinges  11  are  how  many  ? 

43.  Four  times  12  are  how  many  ? 

44.  What  cost  3  quarts  of  cherries,  at  6  cent?  • 
quart  ? 

45.  What  cost  3  lead  pencils,  at  5  cents  a  piece  ? 

46.  What  cost  3  quarts  of  milk,  at  4  cents  a  quart  ? 

47.  What  cost  3  yards  of  ribbon,  at  7  cents  a  yard  ? 

48.  What  cost  4  quarts  of  chestnuts,  at  6  cents  a 
quart  ? 

49.  What  cost  4   yards  of  edging,  at  5  cents  a 
yard? 

50.  What  cost  3  ounces  of  snuff,  at  8  cents  an 
unce? 

51.  What  cost  4  ounces  of  cinnamon,  at  7  cents  an 
ounce  ? 

52.  What  cost  3  pounds  of  cheese,  at  10  cents  a 
pound  1 

53.  What  cost  4  sheets  of  wadding,  at  8  cents  a 
sheet? 

54.  What  cost  3  yards  of  calico,  at  11  cents  a 
yard? 


ARITHMETIC. 


27 


55.  What  cost  4  skeins  of  silk,  at  9  cents  a  skein  ? 

56.  What  cost  3  yards  of  ribbon,  at  12  cents  a 
vard  ? 

57.  What  cost  4  pounds  of  starch,  at  12  cents  a 
oound  ? 

58.  What  cost  4  candlesticks,  at  11  -cents  a  piece 

59.  What  cost  4  tops,  at  10  cents  a  jiece  ? 

60.  What  cost  5  apples,  at  4  cents  a  piece  ? 

61.  Five  times  6  are  how  many  ? 

62.  Five  times  7  are  how  many  ? 

63.  Five  times  9  are  how  many  ? 

64.  Five  times  8  are  how  many  ? 

65.  Five  times  5  are  how  many  ? 

66.  Five  times  10  are  how  many  ! 

67.  Five  times  12  are  how  many? 

68.  Five  times  11  are  how  many  ? 

69.  Six  times  6  are  how  many  ? 

70.  Six  times  8  are  how  many  ? 

71.  Six  times  7  are  how  many  ? 

72.  Six  times  10  are  how  many  ? 

73.  Six  times  9  are  how  many  ? 

74.  Six  times  12  are  how  many  ? 

75.  Six  times  11  are  how  many? 

76.  Seven  times  6  are  how  many  ? 

77.  Seven  times  8  are  how  many  ? 

78.  Seven  times  7  are  how  many  ? 

79.  Seven  times  10  are  how  many  ? 

80.  Seven  times  9  are  how  many  ? 

81  Seven  times  12  are  how  many  ? 

82  Seven  times  11  are  how  many? 

83.  What  cost  5  barrels  of  flour,  at  6  dollars 
barrel  ? 

84.  What  cost  5  bushels  of  potatoes,  ai  5  dimes  a 
bushel  ? 

85.  What  cost  d  primers,  at  6  cents  a  piece  ? 

66.  What  cost  5   barrels  of  fish,  at  7  dollars  a 
barrel  ? 


28  ARITHMETIC. 

87.  What  cost  6  pounds  of  mutton,  at  7  cents  e 
pound  ? 

88.  What  cost  5  barrels  of  sugar,  at  12  dollars  a 
barrel  ? 

89.  What  cost  6  pounds  of  sturgeon,  at  10  cenU  a 
ound  ? 

90.  What  cost  6  pounds  of  almonds,  at  12  cents  a 
pound  ? 

91.  What  cost  5  barrels  of  pork,  at  10  dollars  a 
barrel ? 

92.  What  cost  6  pounds  of  candles,  at  9  cents  a 
pound  ? 

93.  What  cost  5  coats,  at  9  dollars  a  piece  ? 

94.  What  cost  6  handkerchiefs,  at  11  cents  a  piece  ? 

95.  What  cost  6  inkstands,  at  8  cents  a  piece  ? 

96.  What  cost  7  lamps,  at  9  dimes  a  piece  ? 

97.  What  cost  7  plows,  at  8  dollars  a  piece  ? 

98.  What  cost  7  boxes  of  caps,  at  10  cents  a  box  ? 

99.  What  cost  7  quires  of  paper,  at  12  cents  a 
quire  ? 

100.  What  cost  7  letter- folders,  at  11  cents  a  piece  I 

101.  Eight  times  8  are  how  many  ? 

102.  Eight  times  10  are  how  many  ? 

103.  Nine  times  8  are  how  many  I 

104.  Eight  times  7  are  how  many  ? 

105.  Nine  times  9  are  how  many  1 

106.  Eight  times  9  are  how  many  ? 

107.  Nine  times  11  are  how  many? 

108.  Eight  times  12  are  how  many  ? 

109.  Nine  times  10  are  how  many  ? 

110.  Eight  times  11  are  how  many  ? 

111.  Nine  times  12  are  how  many  ? 

112.  What  cost  9  bunches  of  roses  at  9  cents  a 
bunch  ? 

113.  What  cost  8  pen-knives,  at  12  cents  a  piece  I 

114.  What  cost  9  bunches  of  grapes,  at  12  cents  a 
bunch  ? 


ARITHMETIC.  29 

V 

115.  What  cost  11  yards  of  calico,  at  11  cents  a 
yard? 

116.  What  cost  10  balls  of  cotton,  at  12  cents  a 
ball? 

117.  What  cost  11  pounds  of  ginger,  at  12  cents 
pound  ? 

118.  What  cost  10  blocks  of  tape,  at  8  cents  . 
block  ? 

119.  What  cost  12  yards  of  cloth,  at  12  dimes  a 
yard? 

120.  What  cost  13  pair  of  boots,  at  4  dollars  a  pair  ? 


LESSON    II. 

CHAPTERS    FIRST    AND    SECOND    COMBINED   WITH    THE   PRECEDING    LESSON. 

1.  At  7  cents  a  piece,  what  will  9  pine-apples  cost  ? 

2.  If  the  postage  on  1  letter  is  5  cents,  what  will  be 
the  postage  on  8  letters  ? 

3.  If  it  require  8  yards  of  calico  to  make  1  dress, 
how  many  yards  will  it  require  to  make  7  dresses  ? 

4.  If  John  obtain  2  credit-marks  in   1  day,  how 
many  will  he  have  in  15  days  ? 

5.  A  man  hired  a  horse  to  ride,  and  was  to  give  5 
cents  for  every  mile  he  rode; — he  /ode   12  miles; 
how  much  must  he  pay  ? 

6.  Margaret's  cloak  contains  7   yards  of  merino, 
worth  9  dimes  a  yard ;   what  was  the  value  of  her 
cloak  ? 

7.  If  a  stage-coach  go  nine  miles  in  an  hour,  how 
far  will  it  go  in  7  hours  ? 

8.  At  2  dollars  a  week,  what  will  20  weeks   board 
amount  to  ? 

9.  The  fare  by  railroad  from  Albany  to  Boston  is 
5  dollars  for  1  person ;  what  will  it  be  for  a  family  of 
9  persons  ? 


BO  ARITHMETIC, 

10.  Helen  had  8  rose  bushes,  and  there  were  7 
roses  on  each ;  how  many  roses  had  she  in  all  ? 

11.  At  3  dimes  a  gallon,  what  will  15  gallons  of 
molasses  cost  ? 

12.  There  are  10  rows  of  trees  in  an  orchard,  and 
32  trees  in  each  row ;  how  many  trees  are  there  in  the 
orchard  ? 

13.  A  traveller  meeting  13  beggars,  gave  to  each 
of  them  3  dimes ;   how  many  dimes  did  he  give  to 
them  all  ? 

14.  A  woman  bought  11   yards   of  cloth  and  paid 
for  it  with  butter, — giving  9  pounds,  for  a  yard ;  how 
many  pounds  of  butter  did  it  take  to  pay  for  the  cloth  ? 
How  much  did  the  cloth  cost  providing  butter  was 
worth  10  cents  a  pound  ? 

15.  In  a  certain  corn  field  there   are  24  rows,  and 
30  hills  in  each  row  ;  how  many  hills  in  the  field  ? 

16.  What  will  40  steel  pens  cost,   at  2  cents  a 
piece  ? 

17.  What  will  8  pair  of  snuffers  cost,  at  3  dimes  a 
pair? 

18.  When  2  dimes  are  paid  for  1  duck,  what  will 
be  the  cost  of  8  ducks  ?  of  10  ducks  ?  of  12  ducks  ? 

19.  When  hay  is  worth  8  dollars  a  ton,  what  is  the 
value  of  2  tons  ?  4  tons  ?  3  tons  ?  7  tons  ?  5  tons  ?  10 
tons?  12  tons? 

20.  At  2  dimes  a  piece,  what  will  4  books  cost  ?  6 
books?  8  books?  10  books?  12  books?  11  books?  7 
Jboks? 

21.  If  5  cents  will  buy  1  primer,  what  will  je 
the  cost  of  4  primers  ?  of  6  ?  of  9  ?  of  8  ?  of  10  ? 

22.  6  plates  at  5  dimes  a   piece,  will   cost  how 
much? 

23.  At  5  dimes  a  piece,  what  will  4  handkerchiefs 
cost  ?  6  ?  8  ?  10  ? 

24.  At  6  dimes  a  piece,  what  will  2  geese  cost  I 
4?*?8?  10?  12?  9?7? 


ARITHMETIC.  31 

2a    At  12  cents  a  piece,  what  will  3  candlesticks 
«ost*    What  will  6?  5?  8?  9?  10?  7? 

26.  if  I  pay  5  cents  for  riding  1   mile,  how  much 
must  i  pay  for  riding  7  miles  ?   8  miles  ?    9  ?  6  ? 
10?  1*? 

27.  At  7  cents  a  yard,  what  will  5  yards  of  ribbon 
dost  ?  6  yards  ?  8  yards  ?   9  yards  ?   10  yards  ?   12 
yards  ? 

28.  If  a  tooth-brush  cost  18  cents,  what  will  4 
cost? 

29.  9  turkeys  will  cost  how  much^  at  8  dimes  a 
piece  ? 

30.  At  14  cents  a  quire,  what  will  2  quires  of  paper 
cost  ?  3  quires  ?  4  quires  ?  5  quires  ? 

31.  What  will  7  pictures  cost,  at  5  cents  a  piece  ? 
at  6. cents  a  piece  ?  at  8  cents  a  piece  ?  at  10  cents  a 
piece  ? 

32.  What  cost  8  bosoms,  at  6  dimes  a  piece  ?  at  10 
dimes  a  piece  ? 

33.  At  10  dimes  a  piece,  what  will  4  caps  cost  ? 
5  ?  6  ?  8  ?  9  ? 

34.  At  40   cents  a  day,  what  will  2  day's  work 
amount  to  ?  5  days  work  ? 

35.  If  1  paper  of  tobacco  cost  6  cents,  what  will  3 
papers  cost?  5  papers?  8  papers?  12  papers? 

36.  At  7  dollars  a  hundred,  what  will  4  hundred 
feet  of  cedar  boards  cost  ?  9  hundred  feet?  10  hundred 
feet? 

37.  If  1  bushel  of  wheat  cost  60  cents,  what  will " 
bushels  cost  ?  4  bushels  ?  5  bushels  ? 

38.  What  cost  8  muffs  at  5  dollars  each  ? 

39.  What  cost  19  lead  pencils,  at  5  cents  each  ? 

40.  What  cost  11   boxes  of  cheese,  at  4  dollars  a 
box  ?  at  5  dollars  a  box  ?  at  8  dollars  a  box  ? 

41.  What  cost  12  barrels  of  pork,  at  5  dollars  a 
barrel  ?  at  8  dollars  ?  at  9  dollars  ?  at  10  dollars  ? 

42.  What  cost  9  .ons  of  hay,  at  13  dollars  a  ton  ? 


82  ARITHMET/C. 

43.  James  is  9  years  old,  and  his  father  is  4  times 
as  old  as  he  ;  how  old  is  his  father  ? 

44.  Jane's  frock  contains  7  yards  of  silk,  worth  8 
dimes  a  yard  ;  what  was  the  value  of  the  silk  ?     Pro* 
viding  the  making  cost  2  dollars ;   what  was  the  cost 
of  her  dress  ? 

45.  If  a  barrel  of  flour  will  serve  12  men  8  days, 
how  long  will  it  serve  1  man  ? 

46.  If  I  spend  8  dollars?  in  a  month,  and  earn  12 
dollars,  how  much  shall  I    have  at  the  end  of  12 
months  1 

47.  If  I  earn  12  dollars  a  month,  and  pay  25  cents 
a  week  for  washing,  and  2  dollars   a  week  for  board, 
how  much  will   I  have  at  the  end  of  40  weeks  (10 
months)  ? 

48.  If  I  buy  9  tons  of  hay,  at  12  dollars  a  ton,  and 
sell  6  of  them  at  15  dollars  a  ton,  and  the  3  remain 
ing  tons  at  10  dollars  a  ton,  how  much  shall  I  gain  by 
the  operation  ? 

49.  Bought  11   yards  of  broad  cloth  at  4  dollars  a 
yard,  but  being  damaged  I  was  obliged  to  lose  18  dol 
lars  by  the  sale  of  it ;  what  did  I  receive  for  it  ? 

50.  If  I  buy  12  barrels  of  pork  at  8  dollars  a  bar 
rel,  and  sell  it  all  for  108  dollars,  how  much  shall  I 
gain  by  so  doing  ? 

51.  A  man  bought  a  horse  for  80  dollars,  paid  2 
dollars  a  week  for  his  keeping,  and  received  4  dollars 
a  week  for  his  work ; — at  the  expiration  of  10  weeks 
toe  sold  him  for  70  dollars ;  how  much  did  he  gain  by 
ihe  operation  ? 

52.  For  what  must  I  sell  4  barrels  of  wheat  winch 
cost  me  8  dollars  a  barrel,  to  gain  8  dollars  ? 

53.  What  is  the  cost  of  9  cows,  at  25  dollars  each  ? 

54.  Providing  a  hunter  should  kill  5  pigeons  and 
wound  4  every  shot ;  how  many  would  he  kill  and 
wound  by  shooting  8  times  ? 


ARITHMETIC.  33 

55.  If  a  man  travel  29  miles  in  a  day,  how  many 
will  he  travel  in  6  days  ? 

56.  8  months'  wages  will  come  to  how  much,  at  18 
dollars  a  month  ? 

57.  If  10  men  eat  18  pounds  of  butter  in  1  week, 
how  long  would  it  last  1  man  ? 

58.  If  80  dollars  will  pay  for  4  dinners  for  20  mca^ 
how  many  dinners  would  it  buy  for  1  man  ? 

59.  Bought  3  yards  of  cloth  for  a  coat,  at  7  dollars 
a  yard,  the  buttons  and  cord  cost  2  dollars,  buckram 
and  wadding  1  dollar, — paid  for  making  6  dollars ;  for 
what  must  it  be  sold  to  gain  5  dollars  ? 

60.  If  17  men  can  do  a  piece  of  work  in  9  days, 
how  many  days  would  it  take  1  man  to  perform  the 
same  work  ? 

61.  Two    men    start   from  the  same  place,   and 
travel  in  opposite  directions  ; — one  at  the  rate  of  7  miles 
an  hour,  the  other  9  miles  an  hour ;  how  far  apart  will 
they  be  in  2  hours  ? 

62.  Two  men  start  from  the  same  place,  and  travel 
the  same  way  ; — one  at  the  rate  of  3  miles  an  hour,  the 
other  8  miles  an  hour ;  how  far  apart  will  they  be  at 
the  end  of  8  hours  ? 

63.  Two  men  are  50  miles  apart,  and  approach  each 
other  ; — one  at  the  rate  of  2  miles  an  hour,  the  other  3 
miles  an  hour ;  how  far  apart  will  they  be  at  the  end 
of  5  hours  ? 

64.  If  1  orange  is  worth  4  apples,  how  many  apples 
must  be  given  for  13  oranges? 

65.  A   man  earned  80  cents  a  day,  and  paid  50 
cents  a  day  for  his  board  and  washing ;   how  much 
had  he  left  at  the  expiration  of  6  days? 

66.  Jane  bought  4  yards  of  silk  at  2  dollars  a  yard, 
3  shawls  at  10  dollars  each,  and  some  delain  for  10 
dollars ; — she  paid  5  ten  dollar  bills  ;  how  much  ought 
she  to  receive  back  ? 

67.  Mary  bought  5  yards  of  silk  at  8  dimes  a  yard, 


34  A2ITHMETIC. 

9  yards  of  linen  at  9  dimes  a  yard  ;  how  many  yards 
did  she  buy,  and  what  did  they  cost  ? 

68.  In  a  certain  school  there  are  12  girls,  and  3 
times  as  many  boys,  lacking  8 ;  how  many  boys  in 
the  school,  and  how  many  boys  and  girls  together  ? 

69.  John  has  7  books,  and  Mary  has  4  times  aa 
nany,  lacking   18 ;  how  many  has  Mary,  and  how 

many  have  they  both  ? 

70.  Albert  has  9  marbles,  Aaron  3  times  as  many, 
lacking  7,  and  Arnos  has  twice  as  many  as  both,  lack 
ing  8  ;  how  many  have  they  each,  and  how  many  have 
they  together  ? 

71.  Perry  worked  for  Elisha  4  days,  at  6  dimes  a 
day ; — Elisha  gave  him  7  bushels  of  corn  at  3  dimes 
a  bushel ;  how  much  was  then  due  Perry  ? 

72.  A  merchant  bought  25  pounds  of  sugar  for  125 
cents,  and  sold  15  pounds  of  it  at  6  cents  a  pound,  and 
the  remaining  10  pounds  at  4  cents  a  pound ;   how 
much  did  he  gain  by  so  doing  ? 

73.  If  the  interest  on  1  dollar  for  a  year  is  6  cents, 
what  would  be  the  interest  on  13  dollars  for  the  same 
time? 

74.  What  will  27  pounds  of  beef  cost,  at  4  cents  a 
pound  ? 

75.  When  beef  is  5  cents  a  pound,  and  pork  9  cents ; 
how  much  more  will  9  pounds  of  pork  cost  than  9 
pounds  of  beef  ? 

76.  Mary  bought  35  quarts  of  milk,  and  on  her 
vvay  home  spilled  4  times  2  quarts,  lacking  3  quarts; 
how  many  quarts  had  she  remaining  ? 

77.  Henry  is  4  feet  in  height  and  John  is  5 ;  and  5 
times  the  sum  of  their  heights,  considered  as  a  num. 
ber,  is  equal  to  their  father's  age  +  15  years.     Re- 
quired,  the  father's  age. 

78.  If  an  orange  cost  2  cents,  a  lemon  twice  as 
much,  and  a  melon  4  times  as  much  as  the  orange  and 


ARITHMETIC.  3 

lemon  together,  lacking  14  cents,  how  much  more  will 
8  melons  cost  than  3  oranges  and  3  lemons  ? 

79.  James  has  9  walnuts,  John  twice  as  many  lack- 
ing  8,  and  Joseph  twice  as  many  as  both  James  and 
John  -f  7 ;  how  many  has  each,  and  how  many  have 

hey  all  ? 

80.  If  an  apple  cost  2  cents,  an  orange  three  times 
as  much  lacking  4  cents,  and  a  pine-apple  three  times 
as  much  as  the  apple  and  orange  -f-  5  cents,  what  will 
be  the  cost  of  all  three  ? 


CHAPTER    IV. 
LESSON    I. 

1.  4  are  how  many  times  2? 

SOLUTION.— 4  are  as  many  times  2  as  2  is   contained  iu  i,  waick  i 
two  times. 

2.  6  are  how  many  times  2  ? 

3.  8  are  how  many  times  2  ? 

4.  10  are  how  many  times  2  ? 

5.  12  are  how  many  times  2  ? 

6.  14  are  how  many  times  2  ? 

7.  6  are  how  many  times  3  ? 

8.  9  are  how  many  times  3  ? 

9.  12  are  how  many  times  3  ? 

10.  15  are  how  many  times  3  ? 

11.  18  are  how  many  times  3  ? 

12.  21  are  how  many  times  3$ 

13.  24  are  how  many  times  3  ? 

14.  16  are  how  many  times  2  ? 

15.  18  are  how  many  times  2  ? 

16.  20  arfi  hnw  manv  timna  9. 1 


ID.   l«  are  now  many  times  a  f 

16.  20  are  how  many  times  2  ? 

17.  22  are  how  many  times  2? 

18.  24  are  how  many  times  2  ? 
H9.  26  are  how  many  times  2  f 


86  ARITHMETIC. 

20.  28  are  how  many  times  4  ? 

21.  At  2  cents  a  piece,  how  many  apples  can  yoi 
buy  for  4  cents  ? 

SOLUTION.— If  for  2  cents  I  can  buy  1  apple,  for  4  cents  I  cafi  buy  a* 
many  apples  as  2  is  contained  in  4,  which  are  two  times.  There 
fore,  at  2  cents  a  piece,  for  4  cents  I  can  buy  2  apples. 

REMARK.— The  following  solution  is  preferred  to  the  above,  if  the  puptif 
ire  acquainted  with  Fractions. 

SOLUTION. — If  for  2  cents  I  can  buy  1  apple  for  1  cent  I  can  buy  J  of 
aa  apple  ;  and  for  4  cents,  4  times  £,  which  are  ^  or  2  apples. 

22.  At  2  cents  a  piece,  how  many  oranges  can  I 
buy  for  6  cents  ? 

23.  At  2  cents  a  piece,  how  many  peaches  can  be 
bought  for  8  cents  1 

24.  At  3  dimes  a  yard,  how  many  yards  of  calico 
can  be  bought  for  12  dimes  ? 

25.  At  3  cents  a  piece,  how  many  lemons  can  be 
bought  for  9  cents  ? 

26.  At  2  cents  a  yard,  how  many  yards  of  tape  can 
be  bought  for  10  cents  ? 

27.  At  2  dimes  a  bushel,  how  many  bushels  of  ap 
pies  may  be  had  for  12  dimes  ? 

28.  How  many  pounds  of  ginger,   at  2  dimes  a 
pound  may  be  had  for  14  dimes  ? 

29.  How  many  baskets  of  strawberries,  at  3  cents 
a  basket  can  be  had  for  15  cents  ? 

30.  For  16  dollars ;   how  many  yards  of  cloth  can 
be  had,  at  2  dollars  a  yard  ? 

31.  For  18    apples;    how  many  oranges   can  be 
bought,  at  the  rate  of  2  apples  for  1  orange  ? 

32.  How  many  primers,  at  2  cents  a  piece,  can  b 
bought  for  24  cents  ? 

33.  How  many  barrels  of  flour,  at  2  dollars  a  bar 
rel,  can  be  bought  for  20  dollars  ? 

34.  For  22  dollars  ;  how  may  sheep  may  be  bought, 
at  2  dollars  a  piece  ? 

35.  How  many  melons  may  be  had  for  18  dimes,  at 
3  dimes  a  piece  ? 


ARITHMETIC.  87 

36.  At  3  cents  a  piece,  how  many  tops  may  be  had 
for  6  cents  ? 

37.  If  1   peck  of  beans  cost  3  dimes,  how  many 
pecks  can  be  bought  for  21  dimes  ? 

38.  At  3  cents  a  mile,  how  many  miles  can  I  ride 
for  24  cents  ? 

39.  How  many  bushels  of  rye,  at  4  dimes  a  bushel, 
may  be  bought  for  12  dimes  1 

40.  How  many  books,  at  4  dimes  each,  can  be 
bought  for  20  dimes  ? 

41.  8  are  how  many  times  4  ? 

42.  12  are  how  many  times  4  ? 

43.  16  are  how  many  times  4  ? 

44.  10  are  how  many  times  5  ? 

45.  15  are  how  many  times  5  ? 

46.  20  are  how  many  times  5  ? 

47.  28  are  how  many  times  7  ? 

48.  32  are  how  many  times  4  ? 

49.  30  are  how  many  times  5  ? 

50.  35  are  how  many  times  5  ? 

51.  36  are  how  many  times  4  ? 

52.  40  are  how  many  times  5  ? 

53.  44  are  how  many  times  4  ? 

54.  30  are  how  many  times  6  1 

55.  28  are  how  many  times  7  ? 

56.  24  are  how  many  times  8  ? 

57.  36  are  how  many  times  9  ? 

58.  24  are  how  many  times  12  ? 

59.  35  are  how  many  times  7  ? 

60.  38  are  how  many  times  2  ? 

61.  At  5  dimes  each,  how  many  turkeys  can  be  had 
for  25  dimes  ? 

62.  If  the  wages  of  1  day  is  4  dimes,  what  will  De 
the  wages  for  9  days  ? 

63.  How  many  days  will  a  man  be  required  to 
work  for  12  dimes,  if  he  Deceive  4  dimes  a  day  ? 


88  ARITHMETIC. 

64.  If  a  boy  spends  5  cents  a  day,  how  many  days 
will  it  take  him  to  spend  15  cents  ? 

65.  A    boy    had   20    marbles,    and   divided   them 
equally  among  his  5  brothers ;  how  many  did  each 
receive  ? 

66.  A  boy  divided  28  cents  equally  among  4  poor 
women  ;  how  many  cents  did  each  receive  ? 

67.  A  farmer  gave  4  of  his  laborers  32  bushels  of 
corn ;  how  many  bushels  did  each  receive  ? 

68.  If  5  quarts  of  molasses  cost  30  cents,  what  will 
1  quart  cost  ? 

69.  At  5  cents  a  yard,  how  many  yards  of  ribbon 
may  be  had  for  35  cents  ?  how  many  for  50  cents  ? 

70.  How  many  pine-apples  at  8  cents  each,  can  be 
obtained  for  40  cents  ?  for  56  cents  ? 

71.  If  a  man  travel  45  miles  in  9  hours,  how  many 
miles  does  he  travel  in  1  hour  ? 

72.  If  a  man  travel  5  miles  in  an  hour,  how  many 
hours  will  it  take  him  to  travel  40  miles  ? 

73.  How  many  yards  of  cloth  at  4  dollars  a  yard, 
can  you  buy  for  32  dollars  ? 

74.  In  a  certain  orchard  there  are  48  trees  staading 
in  rows,  and  6  trees  in  each  row ;  how  many  rows  are 
there  in  the  orchard  ? 

75.  For  56  dollars,  how  many  barrels  of  pork  can 
be  bought,  at  8  dollars  a  barrel  ? 

76.  If  a  man  can  travel  6  miles  in  an  hour,  how 
long  will  it  take  him  to  travel  42  miles  ? 

77.  How  many  yards  of  cloth  at  4  dollars  a  yard, 
*an  you  buy  for  36  dollars  ? 

78.  A  butcher  gave  39  dollars  for  sheep,  at  the  rate 
^f  3  dollars  a  head  ;  how  many  sheep  did  he  buy  ? 

79.  45  dollars  were  given  for  9  barrels  of  flour ; 
how  much  was  it  a  barrel  ? 

80.  How  long  would  it  take  to  travel  72  miles,  at 
she  rate  of  3  miles  an  hour  ? 


ARITHMETIC. 


LESSON    II. 

1.  20  are  how  many  times  2  ?  4  ?  10  ? 

2.  22  are  how  many  times  11  ? 

3.  24  are  how  many  times  3  ?  4  ?  2  ? 

4.  25  are  how  many  times  5  ? 

6.  28  are  how  many  times  2  ?  7  ? 

6.  30  are  how  many  times  2  ?  3  ?  5  ? 

7.  32  are  how  many  times  2  ?  4  ?  16  ? 

8.  34  are  how  many  times  17  ? 

9.  40  are  how  many  times  2?4?5?8? 

10.  44  are  how  many  times  2  ?  11  ? 

11.  46  are  how  many  times  23  ? 

12.  48  are  how  many  times  2?3?4?6? 

13.  50  are  how  many  times  2?  10  ? 

14.  56  are  how  many  times  2  ?  7  ? 

15.  57  are  how  many  times  3  ? 

16.  60  are  how  many  times  2?3?4?5?6? 

17.  64  are  how  many  times  2  ?  4  ?  8  ? 

18.  66  are  how  many  times  2  ?  3  ?  6  ? 

19.  68  are  how  many  times  2  ?  4  ? 

20.  70  are  how  many  times  10  ?  2  ? 

21.  72  are  how  many  times  2  1  4  ?  6  ?  8  ? 

22.  5  are  how  many  times  2,  and  how  many  re. 
maining  ? 

REMARK.— Whenever  there  is  a  remainder,  it  may  be  mentioned  sbnpif 
U  a  remainder. 

23.  7  are  how  many  times  2  ? 

24.  17  are  how  many  times  4  ?  2  ?  5  ? 

25.  18  are  how  many  times  6  ?  4  ?  2  ? 

26.  34  are  how  many  times  4?6?5?2? 

27.  25  are  how  many  times  5?4?2?3? 

28.  16  are  how  many  times  9?4?8?7? 

29.  32  are  how  many  times  7  ?  5  ?  6  ? 

30.  63  are  how  many  times  9  ?  4  ?  5  ?  6  ? 
81.  74  are  how  many  times  2?4?6?7t 


40  ARITHMETIC. 


32.  80  are  how  many  times  2?3?4?5?6?7?8? 

33.  84  are  how  many  times  2?3?4?5?6?7?8? 

34.  88  are  how  many  times  2?4?3?6?8? 
$5.  37  are  how  many  times  2  ?  6  ?  4  ? 

36    27  are  how  many  times  3  ?  4  ?  8  ? 

37.  15  are  how  many  times  4?6?7?8? 

38.  29  are  how  many  times  2?3?4?5?6?7? 

39.  90  are  how  many  times  2?4?6?8?9?llf 

40.  144  are  how  many  times  2?4?6?8?12? 


LESSON    III. 

1.  At  2  cents  each,  how  many  lemons  can  you  get 
for  14  cents  ? 

2.  How  many  boxes  of  cheese,  at  4  dollars  a  box, 
may  be  had  for  12  dollars  ? 

3.  If  one  hundred  pounds  of  hay  cost  3  dollars,  how 
many  hundred  may  be  had  for  15  dollars  ? 

4.  If  one  barrel  of  flour  support  20  persons  one 
week,  how  many  persons  will  it  support  4  weeks  1 

5.  If  1   man  can  ride  1  mile  for  4  cents,  how  far 
can  2  men  ride  for  80  cents  ? 

6.  If  10  men  accomplish  a  certain  piece  of  work  in 
2  days,  how  long  will  it  take  1  man  to  do  the  same  ? 

7.  If  3  yards  of  cloth  make  one  coat,  how  many 
coats  will  18  yards  make  ? 

8.  If  I  receive  12  dollars  interest  in  one  year,  in 
how  many  years  will  I  receive  144  dollars  interest  ? 

9.  A  man  traveled  7  miles  in  1  hour,  at  the  same 
rate,  how  long  would  it  take  him  to  travel  63  miles  ? 

10.  If  1  cow  cost  13  dollars,  how  many  cows  may 
be  had  for  65  dollars  ? 

11.  How  many  pens  can  you  buy  for  27  cents,  if 
1  pen  cost  3  cents  ?  ' 


ARITHMETIC.  41 

12.  If  8  apples  are  worth  40  chestnuts,  how  many 
chestnuts  is  1  apple  worth  ? 

13.  How  many  cents  is  1  lemon  worth,  if  12  lem 
ons  are  worth  48  cents  ?  % 

14.  What  will  1  cord  of  wood  cost,  if  20  cords  cost 
40  dollars  ? 

15.  If  1  pound  of  beef  cost  7  cents,  what  will  19 
pounds  cost  ? 

16.  For  147  cents,  how  many  pounds  of  sugar  can 
be  bought,  at  7  cents  a  pound  ? 

17.  If  9  yards  of  cloth  cost  53  dollars,  how  must  it 
be  sold  a  yard  to  gain  10  dollars  ? 

18.  If  7  barrels  of  flour  cost  38  dollars,  and  were 
sold,  at  7  dollars  a  barrel,  what  was  the  gain  ? 

19.  How  many  peaches,  at  4  cents  each,  _  may  be 
bought  for  96  cents  ? 

20.  How  many  yards  of  cloth,  at  4  dollars  a  yard, 
can  be  bought  for  116  dollars  ? 

21.  How  many  oranges,  at  3  cents  each,  must  be 
given  for  18  lemons  worth  4  cents  each  ? 

22.  If  15  sheep  cost  75  dollars,  what  will  1  sheep 
cost? 

23.  Which  will  cost  the  most,  4  barrels  of  wheat 
flour  at  9  dollars  a  barrel,  or  12  barrels  of  corn  at 
4  dollars  a  barrel,  and  how  much  ? 

24.  How  many  barrels  of  beef,  at  3  dollars  a  barrel, 
can  be  bought  for  54  dollars  ? 

25.  How  many  pounds  of  £sh,  at  5  cents  a  pound, 
may  be  had  for  95  cents? 

'     26.  At  7  cenis  a  pound,  how  many  pounds  of  lead 
may  be  had  for  84  cents  ? 

27.  How  long  will  it  require  to  travel  105  miles, 
at  the  rate  of  5  miles  an  hour  ? 

28.  A  person  divided  72  peaches  equally  among  6 
boys ;  how  many  did  each  receive  ? 

29.  148  marbles  were  divided  equally  among  some 


42  ARITHMETIC. 

ooys ;  how  many  boys  were  there,  providing  each  boy 
received  2  marbles  ? 

30.  How  many  pounds  of  butter,  at  14  cents  a 
pound,  can  be  bought  for  28  apples,  at  3  cents  each  ? 

31.  At  7  cents  a  bottle,  how  many  bottles  of  in* 
can  you  buy  for  14  sheets  of  paper,  at  2  cents  a  sheet  ? 

32.  In  how  many  days  can  1  man  do  as  much  as  7 
men  in  8  days  ? 

33.  In  how  many  days  can  2  men  do  as  much  work 
as  6  men  can  in  3  days  ? 

34.  In  how  many  days  can  4  men  earn  as  much  as 
8  men  can  in  6  days  ? 

35.  In  how  many  days  can  15  men  earn  as.  much 
as  3  men  can  in  25  days  ? 

36.  In  how  many  months  will  6  horses  eat  as  much 
as  18  horses  will  in  5  months  1 

37.  How  many  men  can,  in  7  days,  earn  as  much 
as  28  men  in  4  days  ? 

38.  In  10  days  6  men  will  earn  as  much  as  how 
many  men  in  5  days  ? 

39.  How  many  yards  of  cloth,  at  4  dollars  a  yard, 
may  be  had  for  4  sets  of  chairs,  at  12  dollars  a  set  ? 

40.  A  farmer  gave  13  barrels  of  flour,  worth  4  dollars 
a  barrel,  for  26  yards  of  cloth ;  how  much  was  the 
cloth  a  yard  ? 


LESSON    IV. 

CHAPTERS    FIRST,    SECOND,    THIRD   AND   FOURTH    COMBINED. 

1 .  4  times  6  are  how  many  times  2  ? 

SOLUTION. — 4  times  6  are  24,    24  are  as  many  times  2  as  2  is  contain^ 
in  24,  whfch  are  12  times. 

2.  4  times  9  are  how  many  times  3  ? 

3.  4  times  8  are  how  many  times  2  ? 


ARITHMETIC.  43 


il. 

12. 
13. 


4.  4  times  10  are  how  many  times  5  ? 

5.  4  times  12  are  how  many  times  6  ? 

6.  4  times  14  are  how  many  times  7  ? 

7.  5  times  9  are  how  many  times  15  ? 

8.  5  times  8  are  how  many  times  4  ? 

9.  5  times  12  are  how  many  times  !*»  ?  6  1 

0.  6  times  7  are  how  many  times  2  \ 

1.  6  times  8  are  how  many  times  12?  3? 

2.  4  times  6  are  how  many  times  8  ? 
ji3.  7  times  15  are  how  many  times  5  ? 

14.  12  times  7  are  how  many  times  21  ? 

15.  8  times  7  are  how  many  times  4? 

16.  How  many  times  12  are  9  times  4? 

17.  How  many  times  10  are  5  times  4  ? 

18.  How  many  times  9  are  3  times  21  ? 

19.  How  many  times  5  are  7  times  15  ? 

20.  How  many  times  9  are  3  times  36  ? 

21.  How  many  times  12  are  9  times  13? 

22.  How  many  times  21  are  9  times  14  ? 

23.  How  many  times  7  are  3  times  14  ? 

24.  How  many  times  5  are  8  times  10  ? 

25.  How  many  times  5  are  10  times  6  ? 

26.  How  many  times  5  are  6  times  15  ? 

27.  10  times  4,  -f-  2  are  how  many  times  7  ?  2  ? 
23.  8  times  9,  —  2  are  how  many  times  5  ? 

29.  12  times  8,  —  8  are  how  many  times  2  ? 

30.  26  times  11,  —  6  are  how  many  times  28  ? 

31.  7  times  8,  -f-  4  are  how  many  times  12? 

32.  6  times  7,  +  4  are  how  many  times  2  ? 

33.  5  times  8,  -f-  8  are  how  many  times  6  ? 

34.  4  times  9,  —  4  are  how  many  times  8  ? 

35.  9  times  5,  —  3  are  how  many  times  7  ? 

36.  7  times  12,  — 14  are  how  many  times  5  ? 

37.  4  times  15,  +  4  are  how  many  times  8  ? 

38.  6  times  7,  -f-  3  are  how  many  times  9  ? 

39.  11  times  13, —  3  are  how  many  times  7  ? 

40.  11  times  15,  +  5  are  how  many  times  17  f 


44  ARITHMETIC. 


LESSON    V. 

FRACTICAL  QUESTIONS  COMBINING  CHAPTERS  THIRD  AND  FOUHTH. 

1.  If  2   apples   cost  4  cents,  what  will  3  apples 
cost? 

SOLUTION. — If  2  apples  cost  4  cents,  1  apple  will  cost  1  half  of  4  cents, 
which  is  -2  cents.  If  1  apple  cost  2  cents,  3  apples  will  cost  3  times  2 
cents,  which  are  6  cents. 

2.  If  2  pears  cost  16  cents,  what  will  5  pears  cost? 

3.  If  4  quinces  cost  12  cents,  what  will  3  quinces 
cost? 

4.  If  6  oranges  cost  18  cents,  what  will  9  oranges 
cost? 

5.  If  7  peaches  cost  21  cents,  what  will  9  peaches 
cost? 

6.  If  4  lemons  cost  24  cents,  what  will  7  lemons 
cost? 

7.  If  3  yards  of  tape  cost  18  cents,  what  will  6 
yards  cost? 

8.  If  7  hair-brushes   cost  28  dimes,  what  will  6 
hair-brushes  cost? 

9.  If  9  yards  of  muslin  cost  108  cents,  what  will 
7  yards  cost? 

10.  If  11  books  cost  44  dimes,  what  will  be  the  cost 
of  7  of  the  same  books  ? 

11.  If  12  ink-stands  cost  96  cents,  what  will  2  cost  ? 

12.  If  10  lead-pencils  cost  30  cents,  what  will  be 
the  cost  of  7?  of  9?  of  2? 

13.  What  will  13  yards  of  silk  cost,  if  5  yards  cost 
45  dimes  ? 

14.  If  a  man  travel  15  miles  in  3  hours,  how  far  at 
this  rate,  can  he  travel  in  9  hours  ?  5  hours  ?  7  hours  ? 

15.  If  the  cartage  of  a  load  of  plaster  20  miles  cost 
4  dollars,  how  far  could  it  be  carried  for  12  dollars? 

16.  How  many  pair  of  pantaloons,  can  be  cut  out 
of  21  yards  of  cloth,  if  3  pair  can  be  cut  out  of  9  yards 
of  the  same  kind  of  cloth  ? 


^ARITHMETIC.  45 

17.  What  will  30  pounds  of  sugar  cost,  if  6  pound* 
Gust  42  cents  ? 

18.  What  will  18  pounds  of  veal  cost,  if  6  pound, 
cost  42  cents  ? 

19.  What  will  75  pounds  of  pork  cost,  if  9  pound 
cost  72  cents  ? 

20.  What  will  20  weeks'  board  come  to,  if  7  weeks 
board  cost  14  dollars  1 

21.  What  will  be  the  wages  for  1  year,  if  4  months 
wages  amount  to  48  dollars  ? 

22.  What  will  be  the  cost  of  25  bushels  of  apples 
if  13  bushels  cost  260  cents  ? 

23.  What  will  14  pounds  of  cheese  cost,  if  6  pounds 
cost  54  cents  ? 

24.  If  7  quarts  of  milk  cost  35  cents,  what  will  36 
quarts  cost  ? 

25.  If  4  men  can  do  a  certain  piece  of  work  in  12 
days,  in  how  many  days  will   3  men  do  the  same 
work  ? 

26.  I  gave  for  a  quantity  of  cotton  72  dollars,  and 
sold  it  for  12  yards  of  cloth ;  what  did  the  cloth  cost 
me  a  yard  ? 

27.  Gave  15  pounds  of  sugar  for  5  pounds  of  but 
ter  ;  how  much  did  the  butter  cost  a  pound,  providing 

8  pounds  of  sugar  were  worth  56  cents  ? 

29.  If  4  chestnuts  are  worth  8  walnuts,  how  many 
walnuts  are  27  chestnuts  worth  1 

29.  If  7  yards  of  broadcloth  are  worth  35  dollars, 
how  many  boxes  of  butter,  at  3  dollars  a  box,  would 

9  yards  of  this  cloth  buy  ? 

30.  A  man  bought  4  barrels  of  flour  for  20  dollars, 
and  gave  3  of  them   for  cider,  at  3  dollars  a  barrel ; 
how  many  barrels  of  cider  did  he  got  ? 

31.  A  man  bought  14  barrels  of  cider  for  56  dol 
lars,  and  gave  5  barrels  of  it  for  cloth,  at  2  dollars  a 
yard  ;  how  many  yards  did  he  receive  ? 

32.  A  merchant,  having  15  yards  of  cloth  worth  75 


48  ARITHMETIC. 

dollars,  gave  10  of  them  for  pork,  wo*th  10  dollars  a 
barrel ;  how  many  barrels  did  he  receive  ? 

33.  When  9  bushels  of  rye  were  worth  45  dimes, 
12  bushels  were  given  for  15  yards  of  cloth  ;  what  did 
Ihe  cloth  cost  a  yard  ? 

34.  If  35  yards  of  cloth  cost  140  dollars,  what  M  ill 
05  yards  of  the  same  cloth  cost? 

35.  Two  boys  are  32  rods  apart,  and  both  running 
in  the  same  direction,  the  hindermost  boy  gains  on  the 
other  4  rods  each  minute  ;  in  how  many  minutes  will 
he  overtake  him  ? 

36.  How  many  boxes  will  be  required  to  contain 
56  bushels,  providing  each  box  contains  8  bushels  ? 

37.  How  many  barrels  of  onions,  at  3  dollars  a  bar- 
rel,  must  be  given  for  21  boxes  of  raisins,  at  2  dollars 
a  box? 

38.  A  farmer  bought  9  yards  of  cloth,  at  4  dollars 
a  yard,  and  paid  for  it  with  cider,  at  3  dollars  a  bar 
rel  ;  how  many  barrels  did  it  take  ? 

39.  How  long  would  it  take  a  man  to  lay  up  24 
dollars,  if  he  save  2  dollars  a  week  ? 

40.  A  farmer  hired  a  laborer  and  agreed  to  give 
him  6  dollars  for  every  3  days'  work ;  how  much  did 
he  receive  a  week,  allowing  6  working  days  in  a 
week  ?  how  much  a  month,  allowing  4  weeks  to  the 
month  ? 

41.  If  4  oranges  are  worth   12  cents,  how  many 
oranges  must  be  given  for  6  pine- apples,  worth  12  cents 
^ach  ? 

42.  How  many  yards  of  cloth,  at  2  dollars  a  yard, 
can  be  bought  for  4  reams  of  paper,  at  5  dollars  a 
ream  ? 

43.  6  men  bought  a  horse  for  80  dollars,  and  paid 
2  dollars  a  week  for  keeping  him ; — at  the  end  of  10 
weeks  they  sold  him  for  82  dollars ;  what  did  each  man 
lose? 

44.  If  2  apples  are  worth  1  orange,  and  2  oranges 


ARITHMETIC.  47 

are  worth  1  lemon  ;  how  many  lemons  can  be  bought 
for  48  apples  ? 

45.  If  5  o-ranges  are  worth   1  pine- apple,   and  2 
pine-apples  are  worth   1  melon ;   how  many  oranges 
may  be  bought  for  4  melons  ? 

46.  A  fox  is  80  rods  before  a  hound,  and  the  hound 
gains  5  rods  on  the  fox  every  10  minutes ;  in  how 
many  minutes  will  the  fox  be  caught  ? 

47.  If  7  men  can  do  a  certain  job  of  work  in  12 
days,  in  how  many  days  could  21  men  do  the  same 
work  ? 

48.  In  how  many  days  can  9  men  do  as  much  work 
as  7  men  can  in  18  days  ? 

49.  How  many  men  can  in  10  days  perform  the 
same  amount  of  work,  that  8  men  can  in  5  days  ? 

50.  Bought  5  firkins  of  butter  for  35  dollars ;   how 
must  it  be  sold  to  gain  10  dollars  ?  what  is  the  gain  on 
each  firkin  ? 


CHAPTER    V. 
LESSON    I. 

TABLE  OF  UNITED  STATES  CURUENGT. 

10  Mills  make  1  Cent,  marked  c. 

10  Cents  "     1  Dime,  "       d. 

10  Dimes  "     1  Dollar,  "        $. 

10  Dollars  "     1  Eagle,  "      E. 

1.  How  many  mills  in  1  cent?  3  cents?  4  cents'? 
J  cents  ? 

2.  How  many  cents  in  1  dime  ?  2  dimes  ?  4  d;mes? 
6  dimes  ?  6  dimes?  9  dimes  ?  10  dimes  ? 

3.  How  many  dimes  in  1  dollar  ?  2  dollars  ?  4  dol 
l*.d  ?  3  dollars  ?  5  dollars  ?  9  dollars  ?  10  dollars  ? 

4.  How  many  eagles  in  400  dimes  1 


48  ARITHMETIC. 

5.  How  many  dimes  in  1  eagle  and  $4  ? 

6.  How  many  dollars  in  40  dimes  ?  90  dimes  ?  80 
dimes  ?  70  dimes  ?  68  dimes  ?  75  dimes  ? 

7.  How  many  cents  in  40  mills  ?    60  mills  ?    50 
mills  ?  80  mills  ?  48  mills  ?  55  mills  ?  47  mills  ? 

8.  If  3  yards  of  muslin  cost  6  dimes,  how  many 
yards  can  be  bought  for  1  dollar  ? 

9.  How  many  pounds  of  pepper  can  you  buy  for  1 
eagle,  if  12  pounds  cost  6  dimes  ? 

10.  How  many  pounds  of  candies  can  you  buy  for 
14  eagles,  if  10  pounds  cost  140  cents  ? 


LESSON    II. 

TABLE  OF  TROT  WEIGHT. 

24  Grains  make  1  Pennyweight,  marked  pwt. 

20  Pennweights      "      1  Ounce,  "        oz. 

12  Ounces  "      1  Pound,  "        Ib. 

1.  How  many  pennyweights  in  240  grains? 

2.  How   many    pennyweights    in    4    ounces  ?  t  5 
ounces  ?  6  ounces  ? 

3.  How  many  ounces  in   1   pound  ?   3  pounds  ?  5 
pounds  ?  8  pounds  ? 

4.  In  24  ounces  how  many  pounds  ?  in  48  ounces  ? 
in  36  ounces  ?  in  60  ounces  ?  in  84  ounces  ? 

5.  How  many  ounces  in  20  pennyweights  1  in  40  ? 
in  60  ?  in  70  ? 

6.  If  7  grains  of  gold  cost  168  dimes,  how  much 
wiL  10  pennyweights  cost? 

7.  What  will    1   pennyweight   of  gold  cost,   if  2 
grains  cost  18  dimes  ? 

8.  How  many  pennyweights  in  4  oz.  and  6  penny, 
weights  ? 

9.  How  many  pounds  in  48  pwt.  ? 

Iff    Hrw  many  grains  in  2  oz.,  2  pwt.  and  2  gr.  ? 


ARITHMETIC. 


LESSON    III.  :. 

TABLE  OF  ATOIRDUPOIS  WEIGHT. 

16  Drams  make  1  Ounce,  ma.~kec   oz. 

16  Ounces  "      1  Pound,  "         Ib. 

25  Pounds  "      1  Quarter,  qr. 

4  Quarters  "      1  Hundred-weight,      "         cwt. 

20  Hundred-weight     "      1  Ton,  T. 

1.  How  many  drams  in  2  ounces  ?  in  4  ?  in  10  ? 

2.  How  many  ounces  in  2  pounds  ?  in  4  ?  in  8  ? 

3.  How  many  quarters   in    100    pounds?    in  400 
pounds  ? 

4.  Plow  many  pounds  in  3  quarters  ?  in  2  ?  in  7  ? 

5.  How  many  quarters  in  2  hundred-weight  ?  in  3  ? 

6.  In  8  qr.  how  many  hundred- weight  ? 

7.  If  30  Ib.  of  hay  cost  6   dimes,  what  will  3  qr. 
Cost? 

8.  What  will  2  tons  of  iron  cost,  if  Impound  cost  1 
dime  ? 

9.  What  will  40  tons  of  hay  cost,  at  2  dimes  a 
quarter  ? 

10.  What  will  2  cwt.  of  sugar  cost,  at  a  dime  % 
pound  ? 


LESSON    IV. 

TABLE  or  CLOTH  MEASURE. 

2^  Inches  make  1  Nail,  marked  na. 

4    Nails        "  ,1  Quarter  of  a  yard,        "       qr. 

4  Quarters  "  "l  Yard,  «       yd. 

3    Quarters  "     1  Ell  Flemish,  «       E.  Fl. 

5  Quarters  "     1  Ell  English,  "       E.  E. 

6  Quarters  "     1  Ell  French,  "      E.  Fr. 

1.  In  4  yds.  3  qr.,  how  many  quarters  ? 

2.  In  7  yds..  2  qr.,  how  many  Ells  French  ? 

3.  In  3  yds.  3  qr.,  how  many  Ells  Flemish  ? 

*: 


50  ARITHMETIC. 

4.  In  8  Ells  English,  how  many  yards  ? 

5.  In  7  Ells  Flemish,  how  many  yards  and  quar 
ters  ? 

6.  In  3   Ells  French,  how  many  yards  and  quas. 
ters  ? 

7.  In  4  Ells  Fr.  and  8  Ells  Fl.,  how  many  yards! 

8.  In  1  qr.,  how  many  inches  ? 

9.  What  will  6  E.  E.  of  cloth  cost,  if  6  nails  cost 
48  cents  ? 

10.  What  will  3  E.  E.  +  2  E.  Fr.  of  cloth  cost, 
if  3  nails  cost  12  cents  ? 


LESSON    V. 

TABLE  OF  WI.TE  MEASURE. 


4  Gills             make  1  Pint, 

marked  pt. 

2  Pints 

'     1  Quart, 

u 

ft 

4  Quarts 

1    1  Gallon, 

K 

gaJ. 

42  Gallons 

'     1  Tierce, 

(t 

frer. 

63  Gallons 

1     1  Hogshead, 

(C 

AM. 

2  Hogsheads 

(     1  Pipe, 

U 

*». 

2  Pipes                      1  Tun, 

U 

Jwn. 

1.  How  many  gills  in  3  pints? 

2.  In  3  qts.,  how  many  gills  ? 

3.  In  12  gallons,  how  many  pints  ? 

4.  What  will  5  gallons  of  rum  cost,  if  3  gills  cost 
5  cents  ? 

5.  How  many  pints  in  2  pipes  ? 

6.  A  merchant  bought  a  hogshead  of  molasses  for 
20  dollars,  and  sold  it,  at  the  rate  df  15  cents  for  3 
pints ;  how  much  did  he  gain  by  the  bargain  ? 

7.  How  much  will  a  gallon  of  wine  cost,  if  7  gills 
cost  21  cents  ? 

8.  In  1  tierce,  how  many  pints  ? 

9.  In  4  quarts  and  2  pints,  how  many  gills  ? 

10.  In  1  tun,  how  many  gills  ? 


ARITHMETIC.  61 


LESSON    VI. 

TABLE  OF  DRY  MEASURE. 

2  Pints  make  1  Quart,  marked  qt. 
S  Quarts  "  1  Peck,  "  pk 
4  Pecks  "  1  Bushel,  "  bu 

1.  In  1  peck,  how  many  pints? 


2.  2  pecks  will  fill  how  many  pint  measures  ? 

3.  In  3  pecks  and  3  quarts,  how  many  pints  ? 

4.  In  1  bushel  and  3  pecks,  how  many  quarts  ? 

5.  In    1    bushel,    how  many   quarts?    how  many 
pints  ? 

6.  If  8  pints  of  nuts  cost  24  cents,  what  will  3 
pecks  cost  at  the  same  rate  ? 

7.  A  market-woman  bought  4  quarts  of  strawber 
ries  for  29  cents,  and  sold  them,  at  5  cents  a  pint ; 
how  much  did  she  gain  ? 

8.  A  person  sold  2  bushels  and  1  peck  of  currants, 
at  2  cents  a  pint,  and  in  payment  received  1  bushel  of 
gooseberries,  at  4  cents  a  pint ;  how  much  remains  due  ? 

9.  What  will  5  quarts  of  wheat  cost,  if  1  bushel 
cost  128  cents  ? 

10.  A  farmer  sold  1  bu.,  3  pk.  and  1  pt.  of  clover, 
seed,  at  640  cents  a  bushel,  and  in  payment  received 
1  bu.,  2  pk.  and  3  quarts  of  grass-seed,  at  820  cents  a 
bushel ;  how  much  remains  due  ? 


LESSON    VII. 

TABLE  OF  TIME. 

60  Seconds                make  1  Minute,  marked  m. 

60  Minutes                    "     1  Hour,  "  h. 

24  Hours                       "     1  Day,  "  d. 

7  Days                        "     1  Week,  "  w. 

4  Weeks                     "     1  Month,  "  mo. 

12  Calendar  months     "     1  Year,  "  y. 

52  Weeks                     "     1  Year,  "  y. 


ARITHMETIC. 


The   following   table    exhibits   the   names   of  the 
months,  and  the  number  of  days  in  each. 

NAMES.  DATS. 

2  (    1  st  month  January, 31 


2d 

3d 

4th 

5th 

6th 
7th 
8th 

9th 
10th 
llth 


February, 28,  in  leap  year  29 

March, 31 

April, 30 

May,          31 

June,  30 

July,  31 

August, 31 

September, 30 

October, 31 

November, 30 


a  j  12th      "      December, 31 


In  our  calculations  on  interest  we  shall  reckon  30 
days  to  the  month,  and  12  months  to  the  year,  although  not 
strictly  accurate. 

1.  In  2  hours  how  many  seconds  ? 

2.  In  2  weeks  and  5  days,  how  many  days? 

3.  In  48  hours,  how  many  days  ? 

4.  7200  seconds,  how  many  hours  ? 

5.  How  many  hours  in  a  week  ? 

6.  In  1  day,  12  hours  and  10  minutes ;  how  many 
minutes  ? 

.   7.  How  many  hours  in  a  month  ? 

8.  If  a  boy  can  do  a  piece  of  work  in  40  minutes, 
how  many  hours  would  it  take  him  to  perform   12 
times  as  much  work  ? 

9.  If  I  can  do  a  piece  of  work  in  10  minutes,  how 
many  hours  would  it  take  to  perform  a  piece  of  work 
12  times  as  large  ? 

10.  How  many  days  in  3  weeks  and  5  days  ? 


ARITHMETIC.  53 

CHAPTER    V    c 
LESSON    I. 

1 .  If  I  cut  an  apple  into  3  equal  parts,  what  is  1  of 
these  parts  called  ?  what  are  2  of  these  parts  called  ? 

AKSWER.-— 1  part  is  called  1  third,  and  2  parts  are  called  twice  1  third, 
which  are  2  thirds. 

2.  Mary  had  4  dresses,  and  Rachel  1  half  as  many  ; 
how  many  had  she  ? 

3.  James  is  8  years  old,  and  John  is  1  half  as  old ; 
how  old  is  John  ? 

4.  Moses  having  2  marbles,  gave  1  half  of  them  to 
his  brother ;  how  many  had  he  left  ? 

5.  If  you  divide  6  apples  equally  between  2  boys, 
what  part  of  them  will  each  have  ? 

6.  What  is  1  half  of  6? 

7.  How  many  halves  in  1  ? 

8.  If  an  orange  cost  8  cents,  and  a  peach  1  half  as 
much.,  what  is  the  cost  of  the  peach  ? 

9.  James  had  12  cakes,  and  John  1  half  as  many ; 
how  many  had  he  ? 

10.  If  3  apples  cost  6  cents,  what  part  of  6  cents 
will  1  apple  cost  ? 

11.  What  is  1  third  of  6? 

12.  What  is  1  half  of  8  ?  10  ?  12  ?  14  ?  16  ?  18  ?  20  ? 

13.  If  3  quarts  of  strawberries  cost  '  8  cents,  what 
part  of  18  cents  will  1  quart  cost?     What  part  of  16 
cents  will  2  quarts  cost  ? 

14.  What  is  1  third  of  18  ?  1  half  of  18  ? 

15.  If  4  pounds  of  raisins  cost  8  dimes,  what  part 
of  8  dimes  will  1  pound  cost  ?  2  pounds  ?  3  pounds  ? 
4  pounds  ? 

16.  What  is  1  fourth  of  8? 

17.  What  is  1  fifth  of  15  ? 


54  ;     ARITHMETIC. 

18.  If  1  fifth  of  15  is  3,  what  is  2  fifths  of  15?  3 
fifths  ?  4  fifths  ?  6  fifths  ?  8  fifths  ? 

19.  What  is  1  sixth  of  12  ? 

20.  If  1  sixth  of  12  is  2,  what  is  2  sixths  of  12  ?  3 
sixths  ?  4  sixths  1  5  sixths  ?  7  sixtns  ?  8  sixths  ? 

21.  What  is  1  seventh  of  21  ? 

22.  If  1  seventh  of  21  is  3,  what  is  2  sevenths  of  21 1 
3  sevenths  ?  4  sevenths  ?  5  sevenths  ?  6  sevenths  ? 

23.  If  you  can  buy  1  pound  of  candies  for  12  cents, 
what  part  of  a  pound  can  you  buy  for  1  cent  ?  for  2 
cents?  for  3  cents?  for  5  cents?  for  8  cents?  for  10 
cents  ? 

24.  If  a  coat  cost  $20,  and  a  pair  of  pantaloons  1 
fourth  as  much,  what  will  the  pantaloons  cost  ? 

25.  If  7  barrels  of  cider  cost  $28,  what  part  of  $28 
will  1  barrel  cost  ?  4  barrels  ?  7  barrels  ?  5  barrels  ? 

26.  What  is  1  seventh  of  $28  ?  2  sevenths  of  28  ?  4 
sevenths  ?  5  sevenths  ?  7  sevenths  ?  6  sevenths  ? 

27.  If  1  pound  of  cheese  cost  6  cents,  what  will  1 
third  of  a  p®und  cost  ?  2  thirds  ? 

28.  If  12  lemons  cost  36   cents,  what  part  of  36 
cents  will   1  lemon  cost  ?   2  lemons  ?   4  lemons  ?    5 
lemons  ?  8  lemons  ?  10  lemons  ?  9  lemons  ?  7  lemons  ? 
14  lemons  ? 

29.  What  is  1  twelfth  of  36  ?  2  twelfths  of  36  ?  4 
twelfths?    5  twelfths?    6  twelfths?    9   twelfths?    10 
twelfths  ?  14  twelfths  ? 

30.  What  do  you  understand  by  1  third  ?  2  thirds  ? 

ANSWER. — When  a  thing  has  been  divided  into  three  equal  parts,  1  c  i 
these  parts  is  called  1  third,  and  2  of  these  parts  are  called  2  thirds. 

31.  What  do  you  understand  by  1  half? 

32.  What   do    you    understand    by    1    fourth  ?    2 
fourths  ?  3  fourths  ? 

33.  What  do  you  understand  by  1  fifth?   2  fifthti? 
3  filths  ?  4  fifths  ? 

34.  How  many  thirds  make  a  whole  1 1 

35.  How  many  fourths  in  1  ? 


ARITHMETIC.  65 

, 

36.  What  do  you  understand  by  2  sixths  ?  4  sixths  1 
5  sixths  ? 

37.  What  do  you  understand  by  3  sevenths?   2 
sevenths  ?  4  sevenths  ?  5  sevenths  ? 

38.  How  many  sixths  in  1  ? 

39.  How  many  ninths  in  1  ? 

40.  How  many  eighths  in  1  ? 

41.  How  many  seve    'is  in  1  ? 

42.  How  many  tenths  in  1  ? 

43.  How  many  twentieths  in  1  ? 

44.  What  do   you   understand  by  7  twelfths?    6 
twelfths  ?  9  twelfths  ?  8  twelfths  ? 

45.  James  had  9  marbles,  and  Jacob  had  2  thirds 
as  many ;  how  many  had  he  ? 

46.  Mary  bought  12  candies,  and  Sarah  bought  2 
thirds  as  many ;  how  many  did  Sarah  buy  ? 

47.  Rachel    has   12    primers,  Mary  3    fourths    as 
many,  and  Anthony  2  thirds  as  many  as  Mary ;  how 
many  have  Mary  and  Anthony  respectively  ? 

48.  Albert  is  15  years  old,  and  Ebenezer  is  4  fifths 
as  old ;  how  old  is  he  ? 

49.  Augustus  has  40  cents,  and  Augusta  has  5 
eighths  as  many ;  how  many  has  she  ? 

50.  Morgan  had  36  marbles,  and  gave  4  sixths  of 
them  to  Martin ;  how  many  did  he  give  to  Martin,  and 
how  many  had  he  left  ? 

51.  Moses  has  24  fire-crackers,  and  Nathan  has  7 
sixths  as  many  ;  how  many  has  he  ? 

52.  Mifflin  had  45  cents,  and  Matthew  had  5  ninths 
as  many  ;  how  many  had  he  ? 

53.  Dubois  is  20  years  old,  and  his  father  is  9  fifths 
as  old ;  what  is  his  father's  age  ? 

54.  A  farmer  had  84  sheep,  and  a  wolf  killed  1 
third  of  them  ;  how  many  had  he  remaining  ? 

55.  In  a  certain  school  there  are  12  girls,  and  7 
fourths  as  many  boys ; — required  the  number  of  boys, 
and  the  number  of  boys  and  girls  together. 


66  ARITHMETIC* 

56.  In  a  certain  recitation  36  questions  were  asked, 
and  1  ninth  of  them  answered  wrong  ;  how  many  were 
correctly  answered  ? 

57.  4  fifths  of  all  the  words  given  out  in  a  spelling 
lesson  were  spelled  correctly,  and  8  were  misspelled ; 
of  how  many  words  did  the  lesson  consist  ? 

58.  Montgomery  bought  9  filberts  for  1  cent;  what 
part  of  a  cent  did  1  cost  ?  2  ?  3  ?  6  ?  7  ?  9  ? 

59.  A   horse  was  bought  for  $6.0,  and  sold  for  7 
fifths  of  what  it  cost ;  how  much  was  the  gain  ? 

60.  A  man  received      140  dollars  for   14  weeks' 
labor,  and  paid  1  fifth  of  it  for  board  \   how  much  did 
he  save  a  week  ? 

61.  9  is  1  fourth  of  what  number? 

62.  How  many  are  7  eighths  of  24  ? 

63.  Mr.  A's  wife  is  40  years  old,  and  9  eighths  of 
her  age  equals  his  ;  what  is  his  age  ? 

64.  What  is  2  ninths  of  36  ?   4  ninths  ?   3  fourths  ? 
4  sixths  ?  5  sixths  ?  4  twelfths  ?  9  twelfths  ? 

65.  3  fourths  of  24  are  how  many  times  3  ? 

66.  How  many  are  3   fourths  of  48  ?   4  sixths  ?  5 
eighths  ?  7  eighths  ?  6  eighths  ?  5  sixths  ?  2  thirds  ? 

67.  3  ninths  of  27  are  how  many?  4  ninths?  7 
ninths  ?  8  ninths  ?  2  thirds  ? 

68.  5  sevenths  of  63  are  how  many  times  3  ? 

69.  3  eighths  of  64  are  how  many  times  6  ? 

70.  9  thirds  of  18  are  how  many  times  3  ? 

71.  4  fifths  of  25  are  how  many  times  2  ? 

72.  6  ninths  of  18  are  how  many  times  6  ? 

73.  7  ninths  of  90  are  how  many  times  2  ? 

74.  4  thirds  of  39  are  how  many  times  2  ? 

75.  15  seventeenths  of  34  are  how  many  times  6 

76.  How  many  times  17  are  17  eighteenths  of  36  ? 

77.  How  many  times  8  are  12  thirteenths  of  26  ? 

78.  How  many  times  5  are  10  thirds  of  36  ? 

79.  How  many  times  4  are  2  thirds  of  27,  —  2  ? 

80.  How  many  times  6  are  3  halves  of  48,  +  12 1 


ARITHMETIC.  5*7 

81.  Stephen  having  40  apples,  gave  3  fifths  of  them 
to  one  companion,  and  3  eighths  of  them  to  another ; 
how  many  had  he  remaining  ? 

82.  A  had  $120  ;  1  third  of  it  he  spent  for  a  watch, 

1  fourth  of  it  for  a  suit  of  clothes,  and  3  tenths  of  it 
for  a  sleigh  ;  how  much  had  he  remaining  ? 

83.  Mr.  B,  being  asked  the  cost  of  his  hat,  replied,  2 
thirds  of  $30  dollars  is  4  times  its  cost ;  required  the 
cost  of  the  hat. 

84.  14  ninths  of  $27  is  equal  to  7  times  the  cost  of 
a  pair  of  boots ;  required  the  cost  of  the  boots. 

85.  An  individual,  having  $90  on  interest,  received 

2  forty-fifths  of  the  principal   for  the  interest;  how 
much  interest  did  he  receive  ? 

86.  The  interest  received  on  $360,  was  1  eighteenth 
of  the  principal ;  what  was  the  interest  ? 

87.  B  is  worth  $2000,  and  3  fourths  of  his  fortune 
is  3  times  A's ;  required  A's  fortune. 

88.  3  eighths  of  the  number  of  hours  in  a  day,  is  3 
times  the  number  of  hours  I  work ;  how  many  hours 
do  I  work  ? 

89.  A  pole,  whose  length  is  16  feet,  is  in  the  air  and 
water ;   and  3  fourths  of  the  whole  length  —  4  feet, 
equals  what  is  in  the  air ;  required  the  length  in  the 
water. 

90.  3  fifths  of  $2000,  +  $120,  equals  B's  fortune ; 
how  much  is  B  worth  ? 

91.  The  building  of  a  certain  house  cost  $560,  and 
4  sevenths  of  this,  +  $80  is  1  tenth  of  the  cost  of  the 
farm  on  which  it  stands.     What  was  the  cost  of  the 
farm  ? 

92.  5  eighths  of  72,  +  13,  are  how  many  times  2? 

93.  The  interest  received  on  $960  dollars  lor  5 
years,  was  equal  to  1  third  of  the  principal ;  wliat  was 
the  interest  yearly  received  ? 

94.  What  will  2  thirds  of  12  pounds  of  coffee  cost, 
at  13  cents  a  pound  ? 


68  ARITHMETIC. 

95.  What  will  3  fourths  of  a  gallon  of  alcohol  cost, 
at  9  cents  a  pint  ? 

96.  What  will  1  sixteenth  of  a  bushel  of  flax-seed 
cost,  at  5  cents  a  pint  ? 

97.  How  much  will  7  fifteenths  of  30  pine-apples 
cost,  at  2  dimes  each  ? 

98;  How  much  will  7  ninths  of  a  hogshead  of  mo 
lasses  cost,  at  4  dimes  a  gallon  ? 

99.  What  will  3  fifths  of  100  oranges  cost,  at  1 
half  dime  or  (5  cents)  each? 

100.  If  1  pennyweight  of  gold  cost  $2,  what  will  2 
fifths  of  an  ounce  cost  ? 

101.  What  will  be  the  cost  of  2  thirds  of  36  pounds 
of  butter,  at  2  dimes  a  pound  ? 

102.  2  thirds  of  24,  +  3  fourths  of  16,  are  how 
many  times  7  ? 

103.  2  thirds  of  30,  +  3  fifths  of  40,  are  how  many 
times  8  ? 

104.  3  sevenths  of  21,  +  3  eighths  of  40,  are  how 
many  times  6  ? 

105.  How  far  can  I  walk  in  3  eighths  of  a  day,  at 
the  rate  of  3  miles  an  hour  ? 

106.  If  Marcus  earn  1  dime  in  an  hour,  how  much 
will  he  earn  in  3  eighths  of  a  day  ? 

107.  If  a  horse  travel  10  miles  in  an  hour,  how 
many  times  10  miles  can  he  travel  in  5  twelfths  of  a 
day? 

108.  How  many  cents  will  1  quart  of  gin  cost,  if  1 
gill  cost  15  mills  ? 

109.  How  rcuny  dollars  will  4  sixths  of  a  pound  of 
gold  cost,  if  1  pennyweight  cost  12  dimes  ? 

110.  How  many  eagles  will  25  fourths  of  a  gallon 
of  brandy  cost,  at  1  half  dime  a  gill  ? 


ARITHMETIC.  59 


LESSON    II. 

1.  If  1  third  of  an  orange  cost  2  cents,  what  will  1 
orange  cost  ? 

SOLUTION.— If  1  third  of  an  orange  cost  2  cents  ;  3  thirds,  which  is  A 
whole  orange,  will  cost  3  times  2  cents,  which  are  6  cents. 

2.  If  1  half  of  a  pound  of  raisins  cost  8  cents,  what 
will  1  pound  cost  ? 

3.  Bought  1  third  of  a  barrel  of  sugar  for  $3  ;  what 
will  2  thirds  of  a  barrel  cost  at  the  same  rate  ? 

4.  If  1  third  of  a  pound  of  pork  cost  5  cents,  what 
will  2  pounds  cost  ? 

5.  2  is  1  third  of  what  number  ? 

6.  5  is  1  half  of  what  number? 

7.  If  1  fourth  of  a  lemon  cost  2  cents,  what  will  1 
cost  ? 

8.  If  1  fourth  of  a  melon  cost  5  cents,  what  will  1  cost? 

9.  3  is  1  fourth  of  what  number  ? 

10.  7  is  1  third  of  what  number? 

11.  12  is  1  fifth  of  what  number? 

12.  7  is  1  fourth  of  what  number  ? 

13.  What  will  4  fifths  of  a  pound  of  cinnamon  cost, 
if  1  fifth  of  a  pound  cost  5  cents  ? 

14.  If  1  fifth  of  a  yard  of  cloth  cost  $2,  what  will 
a  yard  cost  ? 

15.  If  1  sixth  of  a  gallon  of  vinegar  cost  2  cents, 
what  will  a  gallon  cost  ? 

16.  A  man,  being  asked  the  value  of  his  horse,  said 
that  1  eighth  of  its  value  was  $12 ;  what  was  the  value 
of  the  horse  ? 

17.  A  man  gave  15  cents  for  his  lodging,  which 
was  1  seventh   as  much   as  his  breakfast  cost  him ; 
what  did  he  give  for  his  breakfast  ? 

18.  Bought  1  eighth  of  a  yard  of  cloth  for  4  dimes ; 
what  will  a  yard  cost  at  that  rate  ? 

19.  If  1  tenth  of  a  yard  of  cloth  cost  47  cents,  how 
much  is  that  a  yard  ? 


50  ARITHMETIC. 

20.  What  will  1  yard  of  cloth  cost,  if  1  ninth  of  a 
yard  cost  5  cents  ? 

21.  What  will  1  bushel  of  corn  cost,  if  1  seventh 
of  a  bushel  cost  5  cents  ? 

22.  What  will  a  hogshead  of  molasses  cost,  if  1 
eighth  of  a  hogshead  cost  $3  ? 

23.  What  will  be  the  cost  of  2  cords  of  wood,  if  1 
eleventh  of  a  cord  cost  30  cents  ? 

24.  If  1   twelfth  of  the  distance  from  Albany  to 
Wilbraham  is  9  miles,  what  is  that  distance? 

25.  9  is  1  tenth  of  what  number  ? 

26.  15  is  1  seventh  of  what  number? 

27.  16  is  1  fifth  of  what  number? 

28.  12  is  1  fifth  of  6  times  what  number? 

29.  15  is  1  sixth  of  5  times  what  number  ? 

30.  18  is  1  fourth  of  6  times  what  number? 

31.  10  is  1  eighth  of  20  times  what  number? 

32.  15  is  1  seventh  of  5  times  what  number? 

33.  20  is  1  eighth  of  16  times  what  number  ? 

34.  30  is  1  third  of  6  times  what  number  ? 

35.  A  boy's  hat  cost  $3,  which  was  1  fifth  of  the 
cost  of  his  coat.     The  cost  of  the  coat  is  required. 

36.  Mr.  B's  saddle  cost  $9,  which  was  1  fortieth 
of  6  times  the  cost  of  his  horse.     The  cost  of  the  horse 
is  required. 

37.  Henry  gave  5  cents  for  a  piece  of  pie,  which 
was  1  twentieth  of  4  times  as  much  as  his  breakfast 
cost  him ;  what  was  the  cost  of  his  breakfast  ? 

38.  A  man,  being  asked  his  agS,  answered,  that  his 
youngest  son's  age,  was  12  years  which  was  just  1  twelfth 
of  3  times  his  age.     Required  the  father's  age. 

39.  Mrs.  B's  shawl  cost  $9,  which  was  1  tenth  of 
3  times  the  cost  of  her  dress ;  what  was  the  cost  of  her 
dress  ? 

40.  John  says  to  James,  who  is  now  10  years  old, 
your  age  is  1  eighth  of  4  times  my  age.     How  old  is 
John? 


ARITHMETIC.  1 

LESSON     III. 

1.  If  2  thirds  of  a  melon  cost  4  cents,  what  will  1 
melon  cost  ? 

SOLUTION. — If  2  thirds  of  a  melon  cost  4  cents,  1  third  will  cost  1  half  oJ 
4  cents,  which  is  2  cents.  If  1  third  of  a  melon  cost  2  cents,  3  thirds 
which  is  a  whole  one,  will  cost  3  times  2  cents,  which  are  6  cents. 

2.  If  2  thirds  of  an  orange  cost  6  cents,  what  \vili 
1  third  of  an  orange  cost  ? 

3.  If  3  fourths  of  a  pound  of  candies  cost  9  cents, 
what  will  1  fourth  of  a  pound  cost  ? 

4.  If  4  thirds  of  a  pound  of  spice  cost  16  cents, 
what  will  1  third  of  a  pound  cost  ? 

5.  If  3  fourths  of  a  pound  of  cinnamon  cost  12 
cents,  what  will  1  fourth  of  a  pound  cost  ? 

6.  If  $4  will  buy  2  fifths  of  a  barrel  of  fish,  what 
will  1  fifth  of  a  barrel  cost  ? 

7.  What  will  1  sixth  of  a  yard  of  cloth  cost,  if  4 
sixths  of  a  yard  cost  120  cents? 

8.  What  will  1  seventh  of  a  hogshead  of  molasses 
cost,  if  5  sevenths  of  a  hogshead  cost  $15? 

9.  What  will  1  ninth  of  a  pound  of  coffee  cost,  if  8 
ninths  of  a  pound  cost  12  cents? 

10.  If  2  thirds  of  a  barrel  of  fish  cost  $8,  what  will 
1  third  of  a  barrel  cost  ? 

11.  If  1  third  of  a  barrel  of  flour  cost  $3,  what  will 
1  barrel  cost? 

12.  If  2  thirds  of  a  barrel  of  fish  cost  $8,  what  will 
1  barrel  cost? 

13.  If  3  fourths  of  a  bushel  of  wheat  cost  9  dimes, 
what  will  1  bushel  cost  ? 

14.  If  4  fifths  of  a  box  of  raisins  cost  12  dimes, 
what  will  1  box  cost  ? 

15.  If  6  eighths  of  a  yard  of  broadcloth  cost  30 
dimes,  how  many  dollars  will  1  yard  cost  ? 

16.  8  is  2  thirds  of  what  number? 

SOLUTION.— If  8  is  2  thirds  of  some  number,  1  third  of  that  number  ii  1 
half  of  8,  which  is  4  ;  and,  if  1  third  of  that  number  is  4,  3  thirds,  which  it 
that  numtor,  is  3  times  4,  which  ave  12.  Therefore,  8  is  2  thirds  of  13. 


62  Ainmime. 

17.  10  is  2  sevenths  of  what  number  ? 

18.  9  is  3  fourths  of  what  number? 

19.  12  is  3  fourths  of  what  number? 

20.  12  is  6  elevenths  of  what  number  ? 

21.  14  is  7  eighths  of  what  number  ? 

22.  14  is  2  sevenths  of  what  number  ? 

23.  6  is  3  tenths  of  what  number  ? 

24.  9  is  3  sevenths  of  what  number  ? 

25.  15  is  5  sixths  of  what  number  ? 

26.  15  is  3  halves  of  what  number  ? 

27.  18  is  9  eighths  of  what  number  ? 

28.  20  is  5  thirteenths  of  what  number  ? 

29.  24  is  8  fifths  of  what  number? 

30.  26  is  13  ninths  of  what  number? 

31.  2  thirds  of  12  is  2  fifths  of  what  number? 

32.  3  fourths  of  12  is  3  eighths  of  what  number  ? 

33.  3  fourths  of  8  is  2  sevenths  of  what  number  ? 

34.  3  fifths  of  25  is  5  fourths  of  what  number? 

35.  2  sevenths  of  14  is  4  ninths  of  what  number  ? 

36.  4  sevenths  of  21  is  4  fifteenths  of  what  num 
ber? 

37.  2  thirds  of  15  is  5  fourths  of  what  number  ? 

38.  7  eighths  of  48  is  3  halves  of  what  number  ? 

39.  8  ninths  of  36  is  4  fifths  of  what  number? 

40.  7  thirds  of  18  is  3  fifths  of  what  number? 

41.  A  watch  cost  916,  and  3  halves  of  the  cost  of 
the  watch  is  8  thirds  of  the  cost  of  the  chain.     What 
was  the  cost  of  the  chain  ? 

42.  A  horse  was  sold  for  $96,  which  was  8  sevenlhs 
of  what  it  cost ;  what  was  the  cost  of  the  horse  ? 

43.  In  a  certain  school  there  are  36  ladies,  and  5 
fourths  of  the  number  of  ladies  equals  3  fifths  of  tfie 
number  of  gentlemen.     How  many  gentlemen  were 
there  in  the  school  ? 

44.  Mary  is  14  years  old,  and  9  sevenths  of  her  age 
IM  2  thirds  of  Margaret's  age ;  what  was  her  age  ? 

45.  A  piece  of  cloth  containing  12  yards  was  sold 


rag. 
sold 


ARITHMETIC.  63 

for  $60,  which  was  5  fourths  of  what  it  cost ;  what  did 
it  cost,  and  what  was  the  gain  on  each  yard? 

46.  A  has  43  geese,  and  3  fourths  of  his  number  is 
equal  to  9  sevenths  of  B's  number ;  how  many  geese 
hasB? 

47.  The  head  of  a  fish  is  12  inches  long,  and  3 
fourths  of  the  length  of  the  head  is  3  fifteenths  of  the 
length  of  the  body.     Required  the  length  of  the  fish. 

43.  A  farm  was  sold  for  $1200,  which  was  only 
6  sevenths  of  what  it  was  worth.  How  much  was 
lost  by  the  bargain  ? 

49.  848  is  3  fifths  of  the  cost  of  12  yards  of  cloth ; 
how  must  it  be  sold  a  yard  to  gain  $16  on  the  whole? 

50.  A  man  gave  §60  for  a  suit  of  clothes,  which 
was  1  fifth  of  his  yearly  income ;  1  sixth  of  the  re- 
mainder  he  spent  for  a  watch,  and  what  then  remained 
was  4  fifths  of  his  brother's  yearly  income.     What 
was  the  yearly  income  of  each? 


LESSON    IV. 


2  thirds 

is  written  thus   J. 

1  half 

« 

tt 

<i           1 

1  third 

M 

« 

•*•     i- 

1  fourth 

« 

« 

y^    j. 

1  sixth 

« 

« 

*     i- 

1  seventh 

« 

M 

•>i     |a 

3  fourths 

M 

'''3*    - 

H      f- 

7  eighths 

JM 

*JW    ^ 

w      1- 

9  tenths 

tt 

« 

"     A- 

5  sevenths 

tt 

tt 

"      »• 

2  fifths 

tt 

" 

f- 

5  thirds 

tt 

U 

**      1- 

fee. 

M 

M 

"    dtc. 

64  ARITHMETIC. 

REMARK.— The  aaore  expressions  arc  called  fraction*.  The  figure 
above  the  short  horizontal  line  is  called  the  numerator,  and  the  figure 
below  the  line  is  called  the  denominator.  For  example,  in  the  fraction  *  ; 
the  3  is  the  numerator,  and  the  4  is  the  denominator. 

The  denominator  of  a  fraction  shows  into  how  many  parts  the  thing  is 
divided  j  and  the  numerator  shows  how  many  of  these  parts  are  taken. 

1.  If  you  cut  an  orange  into  3  equal  parts,  what 
1  of  these  parts  called  ? 

2.  If  a  lemon  be  cut  into  4  equal  pieces,  what  will 
1  of  these  pieces  be  called  ?  2  ?  3  ?  4  ? 

3.  If  a  bushel  of  apples  be  divided  into  6  equal 
parts,  what  will  1  of  these  parts  be  called  ?  3 1  4  ?  6  ? 

4.  If  a  basket  of  peaches  be  divided  into  8  equal 
parts,  what  will  3  of  these  parts  be  called  ?  5  ?  6 1  7  ? 

5.  How  can  you  find  2  thirds  of  an  apple? 

6.  How  can  you  find  3  fourths  of  an  orange  ? 

7.  In  |-  how  many  times  1  ? 

SOLUTION.— In  1  there  are  2  halves,  therefore  1  half  of  the  number  of 
halves  equals  the  number  of  ones.  1  half  of  4  is  2 ;  therefore,  A  equals  9 

8.  In  -|  how  many  times  1  ? 

9.  In  |  how  many  times  1 1 

10.  In  y  how  many  times  1 1 

11.  In  y  how  many  times  1  ? 

12.  In  y  how  many  times  1 1 

13.  In  -|  how  many  times  1  ? 

14.  In  y  how  many  times  1  ? 

15.  In  |  how  many  times  1  ? 

16.  In  y  how  many  times  1  ? 

17.  In  y  how  many  times  1  ? 

18.  In  y  how  many  times  1  ? 

19.  In  *J  how  many  times  1 1 

20.  In  |   how  many  times  1  ? 

21.  In  y  how  many  times  1  ? 

22.  In  y  how  many  times  1 1 

23.  In  Y  how  many  times  1  ? 

24.  In  y  how  many  times  1 1 


ARITHMETIC. 


25.  In  y  how  many  times  1  ? 
20.  In   £   how  many  times  1  ? 

27.  In  y  how  many  times  1  ? 

28.  In  y  how  many  times  1  ? 

29.  In  y  how  many  times  1  ? 

30.  In  y  how  many  times  1  ? 

31.  In  y  how  many  times  1? 

32.  In  y  how  many  times  1  ? 

33.  In  3/  how  many  times  1  ? 

34.  In  y  how  many  times  1  ? 

35.  In  f  o.  how  many  times  1  ? 

36.  In  f  f  how  many  times  1  ? 

37.  In  f  |  how  many  times  1  ? 

38.  In  J|«  how  many  times  1  ? 

39.  In  ST8  how  many  times  1  ? 

40.  In  6g-3  how  many  times  1  ? 

41.  In  J  how  many  times  1  ? 

42.  In  f  how  many  times  1  ? 

43.  In  y  how  many  times  1  ? 

44.  In  y  how  many  times  1  ? 

45.  In  y  how  many  times  1  ? 

46.  In  y  how  many  times  1  ? 


than 


"•• 

of 


68  ARITHMETIC. 

50.  When  the  denominator  is  greater  than  the  nume 
rator,  what  kind  of  a  fraction  is  it  called  ? 

51.  What  kind  of  a  fraction  is  it  called,  when  the 
numerator  is  larger  than  the  denominator  ? 

52.  Reduce  5-J  to  a  mixed  number , 

53.  Reduce  f  f  to  a  mixed  number  . 

54.  Reduce  9¥4  to  a  mixed  number  , 

55.  Reduce  ^  to  a  mixed  number  , 

56.  Reduce  3/  to  a  mixed  number  , 

57.  Reduce  y  to  a  mixed  number , 

58.  Reduce  778  to  a  mixed  number  . 

59.  Reduce  y  to  a  mixed  number  . 

60.  Reduce       to  a  mixed  number  . 


LESSON    V. 

1.  James  had  f  of  an  apple,  and  John  gave  him  } 
moie  ;  how  many  had  he  then? 

2.  Mary  had  |  of  an  orange,  and  her  father  gave 
her  $  of  an  orange  more ;  how  many  had  she  then  ? 

3.  Robert  had  f  of  a  melon,  and  bought  f  of  another 
one ;  how  much  had  lie  then  ? 

4.  Susan  had  ^  of  a  pint  of  walnuts,  and  gave  3j  of 
a  pint  to  her  sisler ;  how  much  had  she  left  ? 

5.  James  bought  \f  of  a  pound  of  candies,  and  on 
his  way  home  ate  f  of  a  pound ;   how  many  had  he 

eft? 

6.  John  gave  |  oi  a  pound  of  raisins  to  James,  |  of 
pound  to  Mary,  and  kept  j  of  a  pound  himself;  ho-w 

many  had  he  at  first  ? 

7.  Mortimer  gave  f  of  a  dollar  for  a  hat,  $!§•  for  a 
vest,  and  had  $3|  remaining ;   how  much  had  he  at 
first? 

8.  Jane  had  5  pounds  of  cinnamon,  and  Harriet  had 
2}  pounds ;  how  many  more  had  Jane  than  Harriet ) 


ARITHMETIC.  67 

9.  Henry  gave  f  of  a  dollar  for  his  breakfast,  f  of 
«  dollar  for  his  dinner,  and  f  of  a  dollar  for  his  sup. 
per;  how  much  did  his  day's  board  cost  him? 

1°-   I  +  £  are  how  many  ? 

11-  f  +  I  are  how  many? 

12.  £  -f  £  are  how  many? 

13.  1*0  +  rV  are  how  many? 

14.  J  -f  £  are  how  many  ? 

15-  V  +  3  are  how  many? 

16-  V4  +  f  are  how  many? 
I"7-    V4  +  Vfl  are  how  many  ? 
18.  f  +  y  are  how  many? 
I9-  ?  +  f  +  f  are  how  many  ? 

20.  |  -f  |  -f  A  are  how  many? 

21.  T\  -f  JL  +  JL.  are  how  many? 

22.  ^  -f  A  4- 1  are  how  many  i 

23.  |  less  f  are  how  many  ninths 

24.  Y  less  V7  are  how  many  ? 

25.  y  —  |  are  how  many  ? 

26.  Y  —  |  are  how  many  ? 

27.  Y  —  |  are  how  many  ? 

28.  y  —  |  are  how  many  ? 

29.  Y  —  f  are  how  many  ? 

30.  y  —  f  are  how  many  ? 

31.  V  —  V°  are  how  many? 

32.  Y  —  |  are  how  many  ? 

33.  f  |  —  f  i  are  how  many  ? 

34.  f  -f-  J  —  J  are  how  many  ? 

35.  J  +  f  —  |  are  how  many? 

36-  I  +  V7  —  I  are  how  many? 

37-  H  —  T!  +  T!  are  how  many  ? 
83.  f  of  60  —  |  of  24  are  how  many  T 

39.  J  of  40  —  |  of  10  are  how  many  ? 

40.  |  of  15  -f-  |  of  &  —  j  of  12  are  how  many 


(58  ARITHMETIC. 


LESSON    VI. 

1.  At  |  of  a  cent  a  piece,  what  will  2  apples  cost  ? 

SOLUTION. — If  1  apple  cost  §  of  a  cent,  2  apples  will  cost  twice  f  of  a 
Ceat,  which  are  *  or  1|  cents. 

2.  At  |  of  a  cent  a  piece,  what  will  5  apples  cost  ? 

3.  At  f  of  a  dime  a  pound,  what  will  10  pounds  of 
candies  cost  ? 

4.  At  If  dimes  a  pound,  what  will  8  pounds  of 
starch  cost  ? 

5.  At  |  of  a  cent  a  piece,  what  will  25  filberts  cost  ? 

6.  At  |  of  a  dime  a  piece,  what  will  8  chickens 
cost? 

7.  At  |  of  a  dollar  a  yard,  what  will  15  yards  of 
linen  cost  ? 

8.  If  a  man  spend  f  of  a  dollar  a  day,  how  much, 
at  this  rate,  will  he  spend  in  23  days  ? 

9.  If  a  man  receive  f  of  an  eagle  in  a  week,  how 
much  will  he  receive  in  52  weeks  ? 

10.  If  1  pound  of  sugar  cost  1£  dimes,  what  will  12 
pounds  cost  ? 

11.  At  5|  cents  a  pound,  what  will  6   pounds  of 
beef  cost  ? 

12.  At  9f  cents  a  pound,  what  will  8  pounds  of 
pork  cost  ? 

13.  At  6|  cents  each,  what  will  12  lemons  cost? 

14.  At  7  j  cents  each,  what  will  20  rabbits  cost  ? 

15.  At  12£  cents  a  dozen,  what  will  4  dozen  egg* 
cost? 

16.  At  llf  cents  a  pound,  what  will  6  pounds  of 
honey  cost  ? 

17.  At  $7f  a  barrel,  what  will  10  barrels  of  tobacco 
cost? 

18.  At  $9f  a  barrel,  what  will  10  barrels  of  pork 
cost? 

19.  What  will  6  boxes  of  raisins  cost,  at  $3|  a 
box? 


ARITHMETIC*  9 

20.  What  will  14  bushels  of  wheat  cost,  at  $lf  a 
bushel  ? 

21.  .What  cost  7  barrels  of  cider,  at  $3£  a  barrel? 

22.  If  a  barrel  of  flour  cost  $4,  what  will  5£  barrels 
cost? 

23.  5  times  4  and  f  of  4  are  how  many  ? 

24.  7  times  6  and  £  of  6  are  how  many  ? 

25.  9  times  7  and  |  of  7  are  how  many  ? 

26.  12  times  9  and  f  of  9  are  how  many  ? 

27.  5  times  10  and  f  of  10  are  how  many  ? 

28.  13  times  4  and  f  of  4  are  how  many  ? 

29.  8  times  7  and  |  of  7  are  how  many  ? 

30.  10  times  13  and  |i  of  13  are  how  many? 

31.  7  times  20  and  J  of  20  are  how  many  ? 

32.  How  many  are  4  times  |  ? 

33.  How  many  are  4  times  2|  ? 

34.  How  many  are  3  times  4f  ? 

35.  How  many  are  5  times  3^  ? 

36.  How  many  are  7  times  9|  ? 

37.  How  many  are  8  times  12|  ? 
88.  How  many  are  9  times  lOf  ? 

39.  How  many  are  6  times  12|  ? 

40.  How  many  are  12  times  9J  ? 


LESSON    VII. 

1.  If  you  give  to  6  persons,  each  f  of  a  dollar,  how 
niany  dollars  will  it  take  ? 

2.  What  will  be  the  cost  of  4  yards  of  cloth,  at  j 
of  a  dollar  a  yard  ? 

3.  If  1  yard  of  cloth  cost  $lf ,  what  will  10  yards 
cost? 

4.  How  many  oranges  will   it   require  to  give  to 
9  boys,  if  to  one  boy  you  give  11  oranges? 

5.  How  many  barrels  of  flour  docs  that  man  give 
away,  who  gives  to  each  of  12  beggars  |  of  a  barrel  ? 


70  iRITHMETIC- 

6.  Anthony  gave  each  of  his  7  companions  |  of  a 
pound  of  candies,  and   had  1  of  a  pound  left;   how 
many  pounds  had  he  at  first  ? 

7.  Thornton  gave  to  each  of  9  beggars  £  of  a  dollar, 
and  had  $7  remaining ;  how  much  had  he  at  first  1 

8.  James  gave  ^  of  an  orange  to  Jackson,  /7  to 
oseph,  and  f^   to  John  ;  what  part  of  an  orange  had 

he  remaining  ? 

9.  Harmon  meeting  3  poor  women  and  5  poor  men, 
gave  to  each  woman  |  o*f  a  dollar,  and  to  each  man  | 
of  a  dollar,  and  then  had  only  $4  remaining ;  how 
much  had  he  at  first  ? 

10.  How  many  quarts   of  chestnuts  must  that  boy 
have,  who  gives  to  each  of  20  persons  |  of  a  quart, 
and  has  7  quarts  remaining  ? 

11.  Mary  gave  to  each  of  her  12  companions  as 
many  pinks  as  she  then  had  roses,  which  were  2,  and 
had  no  flowers  remaining  but  her  roses.     How  many 
ilowers  had  she  at  first  ? 

12.  What  cost  1  quart  of  vinegar,  if  1  pint  cost  | 
of  a  cent  ? 

13.  If  1  gill  of  molasses  cost  |  of  a  cent,  what  will 
2  quarts  cost  ? 

14.  If  2  pints  of  beans  cost  4  cents,  what  will  1 
peck  cost  ? 

15.  If  3  pecks  of  buckwheat  cost  90  cents,  what 
will  1  pint  cost  ? 

•   16.  What  will  10  yards  of  silesia  cost,  if  1  yard 
cost  18|  cents  ? 

17.  What  will  4|  yards  of  silk  cost,  if  1  yard  cost 
dimes  ? 

18.  What  will  f  of  a  yard  of  muslin  cost,  if  1  yard 
cost  10  cents  ? 

19.  What  will  7  spools  of  thread  cost,  if  1  spool 
cost  7 1  cents  ? 

20.  What  will  8*  yards  of  silk  cord  cost,  at  6  cents 
a  yard  ? 


ARITHMETIC,  71 

21.  If  1  yard  of  wadding  cost  5  cents,  what  will 
9|  yards  cost  ? 

22.  What  will  6f  yards  of  muslin  cost,  if  1  yard 
cost  8  cents  ? 

23.  What  will  8|  pounds  of  veal  cost,  at  5  cents 
pound  ? 

24.  How  much  will  9£  barrels  of  cider  cost,  at  $» 
a  barrel  ? 

25.  What  would  be  the  cost  of  12  window-sash,  at 
$3f  each  '* 

26.  What    will   5f  yards  of  gingham  cost,   at   4 
dimes  a  yard  1 

27.  What  will  be  the  cost  of  13  yards  of  bishop 
lawn,  at  $1/3-  a  yard  ? 

28.  What  will  be  the  cost  of  8  looking  glasses,  at 
815J  a  piece? 

29.  What  amount  of  money  will    be  required  to 
purchase  30  pounds  of  rice,  at  6|  cents  a  pound  ? 

30.  What  will  be  the  cost  of  23  pounds  of  crackers, 
at  8J-  cents  a  pound  ? 

31.  What  will   9  barrels  of  fish  cost,  at  $12|  a 
barrel ? 

32.  If  1  grain  of  gold  cost  9£  dimes,  what  will  1 
pennyweight  cost  ? 

33.  If  1  gold  pen  cost  $2f ,  what  will  6  cost  ? 

34.  How  many  pounds  of  meat,  at  5  cents  a  pound 
can  you  buy  for  $3f  ? 

35.  What  will  be  the  cost  of  3  quarts  of  nuts,  at  64 
cents  a  peck  ? 

36.  If  a  coachman  charge  5£  cents  a  mile,  how 
much  must  that  man  pay  who  rides  12  miles  ? 

37.  How  many  dollars,  dimes  and  cents  will  12 
yards  of  cloth  cost,  at  62  cents  a  yard  ? 

38.  How  many  dollars  and  cents  will  4  pecks  of 
grass  seed  cost,  if  1  pint  cost  5  cents  ? 

39.  How  much  will  13  yards  of  shalloon  cost,  at 
13  j  cents  a  yard  ? 


72  ARITHMETIC. 

40.  What  will  be  the  cost  of  16  bushels  of  potatoes, 
at  2^  dimes  a  bushel  ? 


LESSON     VIII. 

EMARK. — A  traction   may  be  multiplied,    by  multiplying   tha 
r,  (as  you  have  already  observed,)  or  by  dividing  the  denomi 
nator. 

1.  How  many  are  5  times  T\  ? 

SOLUTION. — 5  times  y^  is  \ }  and,  if  5  times  ^  is  |,  5 
times  T4ff  are  4  times  £,  which  are  |  or  2.  Therefore  5 
times  y4^  are  2. 

REMARK. — After  the  pupil  has  become  familiar  with  this  method  of 
solution  the  following  may  be  adopted. 

SOLUTION. — 5  times  T4F  are  f  or  2. 

2.  How  many  are  3  times  ^  ? 

3.  How  many  are  9  times  ^6T  ? 

4.  How  many  are  5  times  TJ  ? 

5.  How  many  are  G  times  TJ  ? 

6.  How  many  are  9  times  T4T  1 

7.  How  many  are  9  times  if  ? 

8.  How  many  are  7  times  |f  ? 

9.  8  times  T^  are  how  many  ? 

10.  11  times  if  are  how  many? 

11.  13  times  if  are  how  many  ? 

12.  2  times  |  are  how  many  ? 

13.  5  times  ij  are  how  many  ? 

14.  6  times  f|  are  how  many  ? 

15.  7  times  f  J  are  how  many  ? 

16.  12  times  ^  are  how  many  ? 

17.  How  many  times  5  are  8  times  f|  ? 

18.  How  many  times  12  are  9  times  Tf  ? 

19.  How  many  times  8  are  11  times  ^|  ? 

20.  How  many^times  100  are  25  times  y/  ? 

21.  How  many  times  20  are  35  times  8T\°  ? 

22.  5  times  y  is  4  times  Mary's  age  ;  what  is  hex 
age? 


ARITHMETIC.  73 

23.  13  times  y/  equals  |  of  the  number  of  dollars 
a   certain   wagon   cost.     Required    the   cost   of  the 
wagon. 

24.  25  times  y/  equals  ^  of  the  number  of  men 
that  Gen.  Santa  Anna  had  at  tne  battle  of  Buena  Vista. 
How  many  men  had  he  ? 

25.  6  times  2T°a°  ls  TT  °f  tne  number  of  men  he  had 
wounded.     How  many  men  were  wounded  ? 

26.  7  times  6|9  is  |  of  the  number  of  men  he  had 
killed.     How  many  were  killed  ? 

27.  4  times  4f  °  is  ^  of  the  number  of  men  that 
Gen.  Taylor  had.     How  many  had  he? 

28.  9  times  6/  is  £  of  the  number  of  men  he  had 
killed.     How  many  were  killed  ? 

29.  8  times  }£  is  |  of  what  number  ? 

30.  4  times  f  f  is  £  of  what  number  ? 

81.  A  laborer  worked  12  months,  at  the  rate  of  $10£ 
a  month  ;  how  much  did  his  year's  wages  amount  to  ? 

32.  If  2  quarts  of  wine  cost  48  cents,  what  will  1 
gill  cost  ? 

33.  How  much  ought  I  to  pay  for  3  oranges,  at  } 
of  a  cent  a  piece  ? 

34.  If  a  certain  piece  of  work  can  be  performed  in 
96  hours,  how  many  days  will  be  required  to  perform 
it  by  working  6  hours  a  day  ? 

35.  If  1  man  can  dig  a  ditch  in  15  days,  how  long 
will  it  take  5  men  to  do  it  ? 

36.  If  a  certain  quantity  of  provision  serve  a  family 
of  4  persons  16  days,  how  long  would  it  last  a  family 
of  8  persons  ? 

37.  If  8  men  can  perform  a  certain  piece  of  work 
in  56  days,  in  how  many  days  can  112  men  do  the 
same  ? 

38.  If  3  men  can  plow  18  acres  in  6  days,  in  how 
many  days  could  9  men  do  the  same  ? 

39.  4  men  can  mow  a  certain  field  in  61  days,  in 
how  many  days  can  5  men  perform  the  same  work  ? 


74  AEITHMETIC. 

40.  A  man  bought  6  barrels  of  cider,  at  $3f  a 
barrel ;  how  many  boxes  of  butter,  at  $4  a  box,  will 
it  take  to  pay  for  it  ? 

41.  A  merchant  bought  6  yards  of  cloth  and  sold  it 
for  $20  which  was  y»  °f  wnat  it  cost ;  what  did  i 
cost  a  yard  ? 

42.  Bought  36  yards  of  cloth,  and  sold  £  of  it  for 
$25,  which  was  f  of  what  it  cost ;  how  much  would 
I  have  gained  by  selling  the  whole  at  the  same  rate  ? 

43.  7  men  in  ^  of  a  day  can  earn  $10,  how  long 
would  it  take  1  man  to  earn  the  same  1 

44.  James  is  3|  years  of  age,  which  is  J  of  the  age 
of  Henry  ;    and  Henry  is  9  times  as  old  as  George. 
What  is  the  age  of  Henry  and  George  respectively  ? 

45.  A  of  36  is  3  times  £  of  what  number  ? 

46.  i  of  32  is  |  of  3  times  what  number  ? 

47.  |  of  60  is  |  of  twice  what  number  ? 

48.  2.  of  40  is  ^  of  as  many  dollars  as  Mr.  B's 
horse  cost ;  what  was  the  cost  of  his  horse  ? 

49.  A  person,  being  asked  his  age,  said,  that  |  of  80 
was  |-  of  ten  times  his  age.     What  was  his  age  ? 

50.  Morgan  is  20  years  old,  and  £  of  his  age  is  4 
of  the  age  of  his  brother.     What  was  his  brother's 
age? 


LESSON    IX. 

1 .  How  many  thirds  are  there  in  3  ? 
SOLUTION. — In  1  there  are  3  thirds,  ap.d  ip  3  fkere  are  3 

times  3  thirds,  which  are  f . 
The  following  solution  is  preferred  to  the  above. 

SOLUTION. — In  1  there  are  3  thirds,  therefore,  3  times 
the  number  of  whole  ones,  equal  the  number  of  thirds.  3 
times  §  are  f . 

2.  How  man)-  fourths  are  there  in  3  ? 

3.  How  many  halves  are  there  in  6  ? 


ARITHMETIC.  75 

4.  How  many  fifths  are  there  in  4  ?  in  5  ? 

5.  How  many  fifths  are  there  in  7  ?  in  8  ? 

6.  How  many  sixths  are  there  in  4  ?  in  3  ?  5  ? 

7.  How  many  sevenths  are  there  in  2  ?  in  4  ?  in  6  ? 

8.  How  many  eighths  are  there  in  7  ?  in  4  ?  in  5  ? 

9.  How  many  fifteenths  are  there  in  2  ?  in  3  ?  in  6? 

10.  How  many  tenths  are  there  in  4  ?  in  6  ?  7  ? 

11.  How  many  fourths  are  there  in  3  and  f  ? 

12.  How  many  thirds  are  there  in  4  and  £  ? 

13.  How  many  th  rds  are  there  in  3  and  |  ? 

14.  How  many  halves  are  there  in  8  and  if 

15.  Reduce  6f  to  an  improper  fraction. 

16.  Reduce  9J  to  an  improper  fraction. 

17.  Reduce  7-f  to  an  improper  fraction. 

18.  Reduce  5J  to  an  improper  fraction. 

19.  Reduce  4f  to  an  improper  fraction. 

20.  Among  how  many  individuals,  can  5-|  bushels 
of  wheat  be  distributed,  providing  each  receives  |  of 
a  bushel  ? 

21.  Among  how  many  boys,  can  7f  oranges  be 
divided,  providing  each  receives  i  of  an  orange  ] 

22.  8  and  £  are  how  many  times  £  ? 

23.  9f  are  how  many  times  f 

24.  9f  are  how  many  times  £  ? 

25.  7J  are  how  many  times  f  ? 

26.  12£  are  how  many  times  £  ? 

27.  7-f  are  how  many  times  ^  1 

28.  7f  are  how  many  times  f  ? 

29.  4f  are  how  many  times  f  ? 

30.  lOf  are  kow  many  times  J  ? 

31.  8$  are  how  many  times  f  1 
82.  12f  are  how  many  times  f  ? 

33.  4  times  3^  are  how  many  times  |  ? 

34.  9  times  1|  are  how  many  times  |  ? 

35.  5  times  6|  are  how  many  times  J  ? 

36.  8  times  8|  are  how  many  times  f  ? 

37.  6  times  2f  are  how  many  times  <$  ? 


76  ARITHMETIC. 

38.  A  boy  distributed  9|  apples  equally  among  his 
companions,  giving  to  each  £  of  an  apple ;  how  many 
companions  had  he  ? 

39.  Homer  distributed  $12£  equally  among  some 
poor  women,  giving  to  each  $lf  ;  how  many  women 
were  there  ? 

40.  Mary  gave  |  of  a  pie  to  each  of  her  9  visitors  ; 
how  many  pies  did  it  take  ? 

41.  Bought  8  yards  of  cloth,  at  $5|  a  yard  ;   how 
many  yards  of  silk,  worth  $11  a  yard  will  it  take  to 
pay  for  it  ? 

42.  Bought  9  yards  of  cloth,  worth  $1£  a  yard,  and 
paid   for  it  with   raisins,  at  $1|  a  box  ;   how  many 
boxes  did  it  take  ? 

43.  How  many  bushels  of  turnips,  at  $|  a  bushel 
can  be  bought  for  8  bushels  of  apples,  at  $f  a  bushel  ? 

44.  How  many  apples,  at  J  of  a  cent  each,  can  be 
bought  for  6  oranges,  at  21  cents  apiece  ? 

45.  How  many  yards  of  cloth,  at  $£  a  yard,  can  be 
bought  for  10  boxes  of  butter,  at  $5f  a  box  ? 

46.  How  many  geese,  at  $f  each,  can  be  bought 
for  14  ducks,  at  $f  apiece  1 

47.  How  many  boxes  of  cheese,  worth  $2^  a  box, 
may  be  had  for  17  boxes  of  butter,  at  $1|  a  box. 

48.  How  many  barrels  of  flour,  worth  $5f  a  barrel, 
may  be  had  for  17  bunches  of  cotton,  at  $1£  a  bunch  ? 

49.  How  many  sheep,  at  $1£  a  head,  may  be  had 
for  8  calves,  at  $3|  each  ? 

50.  How  many  quarts  of  alcohol,  at  £  of  a  cent  a 
pint,  may  be  had  for  12  quarts  of  molasses,  at  4J  cents 
a  quart  ? 


ARITHMETIC.  77 


LESSON    X. 

LESSONS  NINTH    AND    TENTH    COMBINED. 

Qg-  REMARK.— A  fraction  may  be  divided,  by  multiplyirg  the  dencm* 
nator  ;  or  by  dividing  the  numerator. 

1.  If  2  yards  of  cloth  cost  $f,  what  will  1  yard 
cost? 

SOLUTION. — If  2  yards  cost  $£,  1  yard  will  cost  J  of 
$|,  which  is  $J. 

2.  If  3  apples  cost  $  of  a  cent,  what  will   1   apple 
cost? 

3.  If  2  oranges  cost  %  of  a  cent,  what  will  1  orange 
cost? 

4.  If  3  yards  of  cord  cost  }|  of  a  cent,  what  will 
1  yard  cost  ? 

5.  If  2  pounds  of  sugar  cost  8|,   (or  3/    cents,) 
\vhat  will  1  pound  cost? 

6.  If  2   pine-apples  cost  14|  cents,  what  will   1 
pine-apple  cost  1 

7.  If  f  of  a  melon  is  worth  2  oranges,  how  much 
is  1  orange  worth  ? 

8.  If  3  apples  are  worth  If  quinces,  what  is  1 
apple  worth  ? 

9.  How  many  times  7  are  f  i  ? 
10.  How  many  times  13  are  7f  ? 
1 1 »  How  many  times  7  are  9^  ? 

12.  How  many  times  21  are  16J  ? 

13.  How  many  times  8  are  33J  ? 

14.  How  many  times  7  are  10^? 

15.  How  many  times  11  are  40£  ? 

16.  How  many  times  18  are  14|  ? 

17.  How  many  times  3  are  4f  ? 

18  How  many  times  9  are  7f  ? 

19  How  many  times  6  are  6f  ? 

20  How  many  times  15  are 


78  ARITHMETIC. 

21.  If  9  oranges  are  worth  $T9^,  how  many  cents  in 
1  orange  worth  ? 

22.  If  4  boxes  of  figs  cost  |  of  an  eagle,  how  many 
dollars  will  1  box  cost  ? 

23.  If  7  pounds  of  cheese  cost  $T\,  how  many  cents 
vill  1  pound  cost  1 

24.  If  3  cakes  cost  /^  of  a  dime,  what  will  1  cake 
cost? 

25.  If  4  pounds  of  chocolate  cost  4|  dimes,  how 
many  cents  is  that  a  pound  ? 

26.  What  will  1  portfolio  cost,  if  3  cost  -^  of  an 
eagle  ? 

27.  If  8  quarts  of  alcohol  cost  32  dimes,  how  man} 
cents  will  2  gills  cost  ? 

28.  What  will  1  pound  of  sugar  cost,  if  4  pounds 
cost  18|  cents? 

29.  If  6  pounds  of  cheese  cost  31|  cents,  what  will 
I  pound  cost  ? 

30.  If  12  eggs  cost  9J  cents,  what  will  be  the  cost 
of  1  egg  ? 

31.  If  7  yards  of  cloth  cost  $24£,  what  will  1  yard 
cost? 

32.  If  5  silk  shawls  cost  $27£,  how  much  is  that 
apiece  ? 

33.  If  9  pair  of  boots  cost  $32f ,  how  much  is  that 
a  pair  ? 

34.  If  9  oranges  are  worth  30|  walnuts,  how  many 
walnuts  is  1  orange  worth  ? 

35.  A  boy  gave  8  apples  for  18|  marbles,  how 
many  marbles  did  he  get  for  1  apple  1 

36.  A  boy  gave  7  cents  for  17£  crackers;  how 
many  did  he  get  for  1  cent  * 

37.  Mary  gave  10  pins  for  23£  chestnuts;    how 
many  did  she  get  for  1  pin  ? 

38.  If  3  yards  of  broadcloth  are  worth  18|  yards 
of  muslin,  how  many  yards  of  muslin  may  be  had  for 
1  yard  of  broadcloU  ? 


ARITHMETIC.  79 

39.  If  John   can   walk    13  miles  while  Jjsiah   is 
walking  32^  miles,  how  far  can  Josiah  walk  while 
John  is  walking  1  mile  ? 

40.  If  2  chestnuts  are  worth  /^  of  a  cent,  and  20 
chestnuts  are  worth  $  of  a  lemon,  how  many  cents  is 

lemon  worth  ? 

41.  If  2  oranges  cost  f  of  a  cent,  what  will  1  orange 
cost? 

SOLUTION. — If  2  oranges  cost  f  of  a  cent,  1  orange  will 
cost  ^  of  |  of  a  cent,  which  is  |  of  a  cent. 

42.  If  3  yards  of  linen  cost  $f ,  what  will  1  yard 
cost? 

43.  If  7  yards  of  tape  cost  13|  cents,  what  will  1 
yard  cost  ? 

44.  If  2  pints  of  molasses  cost  1|  dimes,  how  much 
will  1  gallon  cost  ? 

45.  How  many  times  8  are  6^? 

46.  How  many  times  6  are  5|  ? 

47.  How  many  times  4  are  4J  ? 

48.  How  many  times  2  are  13^? 

49.  How  many  times  7  are  7|  ? 

50.  How  many  times  8  are  9  times  f }  ? 

REMARK.— Multiply  as  in  Lesson  Eighth. 

51.  How  many  times  3  are  6  times  1 

52.  How  many  times  9  are  10  times 

53.  How  many  times  7  are  5  times  3 

54.  How  many  times  5  are  15  times 

55.  How  many  times  7  are  15  times 

56.  How  many  times  5  are  3  times  2|  ? 
67.  How  many  times  6  are  4  times  5|  ? 

58.  If  1|  yards  of  clota  are  worth  $2£,  what  is  I 
yard  worth  ? 

59.  If  6|  bunches  of  grapes  are  worth  40   cents, 
how  many  cents  is  1  bunch  worth  ? 

60.  If  3|  baskets  of  peaches  are  worth  f  5|,  what 
is  1  basket  of  peaches  worth  ? 


80  ARITHMETIC. 

LESSON    XI. 

1.  What  is  £  of  2? 

SOLUTION. — £  of  1  is  ^ ;  and,  if  §  of  1  is  J,  J  of  2  is 
*wice  j,  which  are  f .     Therefore  £  of  2  is  f  of  1. 

2.  What  is  i  of  4  ?  of  8  ? 

3.  What  is  i  of  2  ?  3  ?  5  ?  7  ?  9  ? 

4.  What  is  |  of  3  ?  5  ?  7  ?  9  ?  11  ? 

5.  What  is  J-  of  2?  3?  4?  7?  8? 

6.  What  is  £  of  2  ?  3  ?  5  ?  7  ?  9  ? 

7.  What  is  |  of  2?  3?5?4?6?9?11? 

8.  What  is  1  of  2  ?  4  ?  3  ?  5  ?  6  ?  7  ?  9  ? 

9.  What  is  £  of  2?  4  ?  7  ?  6  ?  3  ?  12  ?  11  ? 

10.  What  is  TL  of  7?  2?  4  ?  6  ?  9  ?  14  ?   15  ? 

11.  If  2  apples  cost  3  cents  what  will  1  apple  cost  ? 

SOLUTION. — If  2  apples  cost  3  cents,  1  apple  will  cost  -J 
of  3  cents,  which  is  f,  or  l£  cents. 

12.  If  2  apples  cost  5  cents,  what  will  1  apple  cost  ? 

13.  If  3  pens  cost  8  cents,  what  will  1  pen  cost? 

14.  If  3  yards  of  tape  cost  14  cents,  what  will  1 
yard  cost  ? 

15.  If  5  barrels  of  flour  cost  $21,  what  will  1  bar 
rel  cost  ? 

16.  If  7  pecks  of  dried  apples  cost  23  dimes,  what 
will  1  peck  cost  ? 

17.  If  4  chickens  cost  9  dimes,  what  will  1  chicken 
cost? 

18.  What  will   1   pound  of  tamarinds  cost,  if  6 
pounds  cost  27  dimes  ? 

19.  What  will  1  barrel  of  flour  cost,  if  3  barrels 
cost  $25  ? 

20.  If  you  divide  7    bushels   of  wheat,   equally, 
among  5  persons,  how  much  will  each  receive? 

21.  Joshua  had  13  marbles,  and  Lewis  had  J  as 
many  +  £  of  a  marble  ;  how  many  had  he  ? 


ARITHMETIC.  81 

22.  A  merchant  divided  3  barrels  of  flour,  equally, 
among  1 1  families ;  what  part  of  a  barrel  did  each 
receive  ? 

23.  A  farmer  divided  5  bushels  of  rye,  equally, 
among  7  of  his  poor  neighbors ;  what  part  of  a  bushel 
did  he  give  to  each  ? 

24.  Calvin  had  4  pints  of  nuts,  and  shared  them, 
equally,  with  6  of  his  companions  ;  how  much  did 
each  receive  ? 

25.  Margaret,    having    7    quarts   of   raspberries, 
shared  them,  equally,  with  8  of  her  playmates ;  what 
part  of  a  quart  did  each  receive  ? 

26.  What  will  1  pound  of  prunes  cost,  if  5  pounds 
cost  48  dimes] 

27.  What  will  2  boxes  of  figs  cost,  if  7  boxes  cost 
29  dimes  ? 

28.  What  will  4  quarts  of  strawberries  cost,  if  9 
quarts  cost  7  dimes  ? 

29.  What  is  1  of  2  ? 

30.  If  i  of  2  is  |,  what  is  |  of  2  ? 

31.  What  is  |  of  4?  of  5?  71  8? 

32.  What  is  |  of  3  ?  of  5  ?  6  ?  7  ? 

33.  What  is  f  of  2  ?  of  3  ?  41  9  ? 

34.  What  is  J-  of  2?  of  3?  5?  7? 

35.  What  is  4  of  3?  of  5?  8?  9? 

36.  What  is  J  of  4?  of  6?  8?  12? 

37.  What  is  f  of  3  ?  of  5  ?  6  ?  9  ? 

38.  What  is  ^T  of  2 ?  of  4?  5?  6? 

39.  What  is  A  of  2?  of  4?  3?  9? 

40.  What  is  T70-  of  71  of  8?  9?  12? 

41.  What  will  |  of  a  pound  of  candies  cost,  if  i 
pound  costs  2  djjnes  ? 

42.  What  will  be  the  cost  of  J  of  a  box  of  raisins/ 
if  1  box  cost  $3  ? 

43.  What  will  be  the  cost  of  }  of  a  yard  of  cloth, 
at  7  dimes  a  yard  ] 


82  ARITHMETIC. 

44.  If  a  ton  of  hay  cost  $10,  what  will  2f  tons 
cost? 

45.  Jeremiah  is  91  years  old,  and  %  of  his  age 
equals  the  age  of  his  oldest  son  ;  how  old  is  he  ? 

46.  Bought  24  yards  of  cloth  for  $48  ;  but,  being 
damaged  I  sold  f  of  it,  at  $lf  a  yard,  and  the  re. 
attainder  for  what  it  cost.     How  much  did  I  lose  ? 

47.  Bought  14  yards  of  cloth ;  and  sold  ^  of  it,  at 
$2  a  yard,  which  amounted  to  $2  less  than  the  whole 
piece  cost.     What  did  it  cost  a  yard  ? 

48.  A  horse  was  sold  for  $97,  which  was  If  times 
as  much  as  it  cost.     What  did  the  horse  cost  ? 

49.  If  9  yards  of  cloth  cost  $17,  what  will  3  yarda 
cost? 

50.  If  7  yards  of  cloth  cost  $25,  what  will  9  yards 
cost? 

51.  What  will  2  pounds  of  opium  cost,  if  5  pounds 
cost  $42  ? 

52.  If  5  pounds  of  indigo  cost  $32,  what  will  2 
pounds  cost? 

53.  A  wagon  was  sold  for  $90,  which  was  {  oi 
tvhat  it  cost.     How  much  did  it  cost  ? 

54.  Two  men  started  from  the  same  place,   and 
raveled  the  same  way  ;  one  at  the  rate  of  92  miles 

:n  10  hours  ;  the  other  at  the  rate  of  ly1^  miles  in  |  of 
in  hour ;  how  far  apart  will  they  be  in  2  hours  ? 

55.  By  a  pipe  4$  gallons  of  water  run  into  a  cis 
tern  in  1  minute  ;  how  much  did  the  vessel  hold  pro- 
viding  it  was  filled  in  9  minutes? 

56.  If  4  men  can  perform  a  ceitain  piece  of  work 
fn  13$  days  ;  how  long  would  it  take  7  men  to  do  the 
same  ? 

57.  If  5  persons  consume  a  barrel  of  flour   in  9 
weeks,  what  part  of  a  barrel  would  they  consume  in 
5  weeks  ? 

58.  If  a  man  earn  $  J  in  a  day,  and  a  boy  $},  bow 
much  will  they  both  earn  in  6  days  ? 


ARITHME11C.  83 

59.  Anthony  spent  -f  of  all  his  money,  ana  the  re 
mainder  he  gave  for  8  yards  of  cloth,  at  $2|  a  yard ; 
how  much  had  he  at  first  ? 

60.  From  a  piece  of  cloth  a  tailor  cut  5  garments, 
each  containing  3f   yards;   and  there  remained  2f 
yards ;  how  many  yards  did  the  piece  contain  ? 

01.  What  will  9  pounds  of  rice  cost,  if  7  pounds 
cost  43  cents  ? 

62.  An  individual,   after  spending  |^  of  all    his 
money,  had  only  $40  remaining ;  how  much  had  he 
at  first  ? 

63.  An  old  lady  bought  30  eggs,  at  the  rate  of  2 
for  5  cents ;  what  did  they  cost  ? 

64.  What  will  13  pounds  of  coffee  cost,  if  26  pounds 
cost  $7  ? 

65.  What  will  7  gallons  of  molasses  cost,  if  6  pints 
cost  27  cents  ? 

66.  If  5  lamps  cost  $7£,  what  will  7  lamps  cost  ? 

67.  If  5  horses  can,  in  4|  days,  consume  20  bushels 
of  oats,  in  how  many  days  can  11  horses  consume  the 
same  ? 

68.  If  15  gold  pens  cost  $20,  what  will  5  of  them  cost  ? 

69.  If  J  of  an  acre  of  land  be  worth  $14,  what  are 
10  acres  worth  ? 

70.  $25  is  4  of  the  cost  of  B's  watch  ;  what  was  the 
cost  of  his  watch  ? 

71.  Mortimer's  hat  cost  $5,  and  f  of  the  cost  of  his 
hat  is  T\j-  of  the  cost  of  his  coat ;   what  was  the  cost 
of  his  coat  ? 

72.  If  a  man  in  -fa  of  a  day  walk  8  miles,  how  far 
can  he  walk  in  5  days  ? 

73.  From  a  piece  of  cloth  containing  20  E.  Fr.,  a 
tailor  cut  8  suits  of  clothes,  each  containing  2J  yards ; 
how  many  yards  remained  ? 

74.  If  a  man  can  cut  1  cord  of  wood  in  5  hours, 
how  many  cords  can  he  cut  in  4  days,  by  working  12 
hours  a  day  / 


84  ARITHMETIC. 

75.  A  man  bought  7  sheep,  at  the  rate  of  9  for 
;  what  did  they  cost  him  ? 

76.  A  boy  bought  13  oranges, — giving  9  apples  foi 
3  oranges;  how  many  apples  did  his  oranges  cos* 
him? 

77.  If  25  cents  buy  7  lemons,  how  many  cents  will 
9  lemons  cost  ? 

78.  |  of  45  equals  f  as  many  dollars  as  Andrew 
has ;  how  many  dollars  has  he  ? 

79.  $30f  is  |  of  all  the  money  A  had  ;   how  much 
had  he  ? 

80.  What  will  3  pecks  of  flax-seed  cost,  if  3  pints 
cost  3  dimes? 

81.  What  will  1  quart  of  cloverseed  cost,  if  2  pecks 
cost  $3  and  2  dimes  ? 

82.  4^  times  7  is  |  of  what  number  ? 

83.  £  of  36  is  J  of  what  number  ? 

84.  i  of  36  is  L2  times  what  number  ? 

85.  |  of  A's  age  is  3  times  B's  age ;  and  B  is  9 
years  old.     What  is  A's  age  ? 

86.  An  individual,  being  asked  the  number  of  hours 
he  labored  each  day,  answered,  1|  times  the  number 
of  hours  in  a  day  is  3  times  as  many  hours  as  I  labor. 
How  many  hours  did  he  labor  each  day  ? 

87.  |  of  15  is  f  of  what  number? 

88.  -|  of  21  is  1£  times  what  number? 

89.  |  of  24  is  If  times  what  number? 

90.  Wright  is  16   years  old,  and   If  times  his  age 
is  t§  times  Charles'  age.     How  old  is  Charles? 

LESSON    XII. 

LE3SONS    EIGHTH,    NINTH    AND    TENTH    COMBINED. 

{ftp-  REMARK. — Pupils  must  exercise  their  own  judgment  in  employing 
the  shortest  of  the  methods  given  in  lessons  eighth  and  enth,  for  multiplying 
and  dividing. 

1.  If  3  barrels  of  flour  cost  $13  J,  what  will  6  barrels 
cost? 


ARITHMETIC.  85 

2.  If  5  pounds  of  opium  cost  $27£,  what  will  20 
pounds  cost  ? 

3.  If  3  pounds  of  sugar  cost  17£  cents,  what  will  8 
pounds  cost  ? 

4.  If  9  pencils  cost  20J  cents,  what  will  12  cost  ? 

5.  How  many  chestnuts  will  pay  for  9  walnuts,  if 
7  chestnuts  are  worth  lOf  walnuts  ? 

6.  If  8  barrels  of  flour  cost  $33£,  what  will  20 
barrels  cost  ? 

7.  If  it  require  9f  yards  of  cloth  to  make  3  coats, 
how  many  yards  will  it  require  to  make  8  coats  ? 

8.  If  8  men  can  perform  a  certain  piece  of  work  in 
Of  days,  how  long  will  it  take  5  men  to  perform  the 
same  ? 

9.  What  will  be  the  cost  of  6  sheep,  if  15  cost  $10£  ! 

10.  If  1  person  consume  10^  bushels  of  wheat  in 
a  month,  how  much  will  13  persons  consume  in  the 
same  time  ? 

11.  If  9J  cents  will  buy  4  peaches,  what  will  be 
the  cost  of  9  peaches  ? 

12.  If  $9TL-  will  pay  for  5  weeks'  board,  how  many 
dollars  will  pay  for  8  weeks'  board  ? 

13.  If  6  orifices  will  fill  a  vessel  in  3|  hours,  how 
many  of  the  same  size  will  be  required  to  fill  it  in  T*j  of 
an  hour  ? 

14.  If  9  men  can  build  a  boat  in  5jf  days,  in  how 
many  days  could  6  men  build  it  ? 

15.  If  2  men  in  4  days  can  earn  $12,  how  many 
dollars  can  7  men  earn  in  the  same  time  ? 

16.  If  I  pay  17|  cents  for  riding  4  miles,  how  much 
must  I  pay  for  riding  6  miles  ? 

17.  What  will  1  year's  board  come  to,  at  $5f  for 
4  weeks  ? 

18.  If  9  barrels  of  fish  cost  $54£,  what  will  27  bar- 
rels  cost  ? 

19.  How  many  dollars  will  1  barrel  of  tobacco  sost 
if  17  barrels  cost  51.J  eagles  ? 


88  ARITHMETIC. 

20  If  13  pounds  of  tea  cost  10}  dimes,  what  will  5 
pounds  cost  ? 

21.  If  7f  tons  of  hay  keep  6  horses  through  the 
winter,  how  many  tons  will  keep  9  horses  the  same 
time  ? 

22.  If  a  fox  is  40  rods  before  a  hound  and  runa 
only  3  rods  to  the  hound  5,  how  many  rods  will  the 
hound  run  before  he  overtakes  the   fox  ? 

23.  How  many  dollars  will  a  man  earn  in  14  days, 
if  he  earn  $3f  in  4  days  ? 

24.  A  merchant  bought  8  pieces  of  cloth,  each 
piece  containing  5  yards  for  $32i  ;  how  much  did  it 
cost  apiece,  and  how  much  a  yard  ? 

25.  If  in  a  certain  time  6  horses  eat  14|  bushels  of 
oats,  how  many  bushels  will  8  horses  eat  in  the  same 
time? 

26.  A  boy  sold  3  lemons,  at  the  rate  of  6  for  8 
cents  ;  what  did  he  receive  for  them  ? 

27.  A  boy  gave  4£  cents  for  some  oranges,  at  the 
rate  of  5  oranges  for  7£  cents ;  how  many  did  he 
buy? 

28.  If  a  piece  of  mahogany  weighing  9  pounds,  is 
worth  $2|,  what  is  the  value  of  12  pounds,  at  the 
eame  rate  ? 

29.  If  a  pole  8  feet  long  cast  a  shadow  4f  feet,  what 
will  be  the  length  of  the  shadow  of  a  pole  which  is  15 
feet  long,  at  the  same  time  of  day  ? 

30.  At  a  certain  time  of  day,  a  pole  5  feet  long 
casts  a  shadow  7ifeet ;  what  is  the  length  of  that  pole 
which,  at  tne  same  time,  casts  a  shadow  \\  feet? 

31.  If  it  require  $21 J  worth  of  provision  to  serve  £ 
men  2  days,  how  many  dollar's  worth  will  serve  5  mei 
1  day? 

32.  What  is  the  length  of  a  pole  the  shadow  of  which  is 
12  feet  long,  at  the  same  time,  a  pole  2|feet  in  length, 
casts  a  shadow  4  feet  long  ? 


ARITHMETIC.  87 


LESSON    XIII. 

REMARK.— By  inspecting  Lessons  8th  and  10th,  we  observe,  that,  mul 
tiplying  both  numerator  and  denominator  by  the  same  number,  does  not 
alter  the  value  of  the  fraction.  Hence,  to  convert  a  fraction  to  an  equiva 
lent  fraction  having  a  different  denominator,  we  may  multiply  both  nu 
merator  and  denominator  by  any  number  which  will  cause  the  fraction 
Co  have  the  required  denominator. 

1.  James  gave  his  sister  £  of  an  apple ;  how  many 
fourths  was  that  ? 

2.  £  is  how  many  sixths  ? 

3.  Byron  gave  his  sister  £  of  an  apple,  and  his 
brother  J  of  an  apple ;  how  many  fourths  did  he  give 
away  ? 

4.  I  is  how  many  sixths  ? 

5.  i  is  how  many  sixths? 

6.  \  and  ^  are  how  many  sixths? 

7.  |  are  how  many  sixths  ? 

8.  £  are  how  many  twelfths  ? 

9.  f  are  how  many  twelfths  ? 

10.  £  are  how  many  eighteenths  ? 

11.  |  are  how  many  tenths  ? 

12.  |  are  how  many  tenths  ? 

13.  A  are  how  many  twentieths  ? 

14.  \  is  how  many  tenths  ? 

15.  HafFord  gave  f  of  an  orange  to  his  sister;  how 
many  fifteenths  did  he  give  away  ? 

16.  How  many  sixteenths  in  £  ? 

17.  How  many  sixteenths  in  f  ? 

18.  How  many  sixteenths  in  £  ? 

19.  How  many  fourteenths  in  %  1 

20.  How  many  fourteenths  in  fy  1 

21.  How  many  fourteenths  in  ^  ? 

22.  How  many  ninths  in  |  ? 

23.  How  many  twentieths  in  J  ] 

24.  How  many  fortieths  in  J  ? 
25*  How  many  forty-ninths  in  f  ? 


88  ARITHMETIC 

26.  How  many  fifteenths  in  f 

27.  A  man  gave  1  of  a  bushel  of  potatoes  to  one 
poor  woman,  and   y3,    of  a  bushel  to  another ;   what 
part  of  a  bushel  did 'he  give  to  both? 

28.  How  could  you  divide  an  apple  so  as  to  give  j 
of  it  to  one  boy,  and  J  of  it  to  another  ? 

29.  ±  -f  |  are  how  many  sixths  ? 

30.  f  +  |  are  how  many  twelfths  ? 

31.  J-  +  i  are  how  many  eighteenths? 

32.  J  +  |  are  how  many  twenty- fourths  ? 

33.  -2  are  how  many  times  ¥3T  ? 

34.  What  is  the  sum  of  f  and  f  ? 

35.  What  is  the  sum  of  ^  and  f  ? 

36.  What  is  the  sum  of  -i  and  *  ? 

37.  What  is  the  sum  of  f  and  f  ? 
39.  What  is  the  sum  of  -f  and  f  ? 

39.  What  is  the  sum  of  1  and  | .? 

40.  What  is  the  sum  of  |-  and  |  ? 

41.  What  is  the  sum  of  J  and  £  ? 

42.  What  is  the  sum  of  f  and  4  ? 

43.  What  is  the  sum  off,  i  and  f  ? 

44.  What  is  the  sum  of  £,  |  and  |  ? 

45.  From  J  subtract  i, 

46.  From  |  subtract  f . 

47.  From  ^  subtract  |. 

48.  From  2|  subtract  nf. 

49.  From  4  subtract  -i. 

50.  From  3  subtract  f . 

51.  From  9  subtract  -if. 

52.  From  5  subtract  |. 

53.  From  3  subtract  1|. 

54.  From  9  subtract  2|. 

55.  From  6  subtract  3J. 


ARITHMETIC. 


56.  14  —  3J  are  how  many  ? 

57.  7  —  2f  are  how  many  ? 

58.  9  —  34  are  how  many  ? 

59.  10  —  3f  are  how  many  ? 

60.  12  —  3£  are  how  many  ? 

61.  13  —  7/j-  are  how  many  ? 

62.  9|  — 4£  are  how  many  ? 

63.  7|  —  5^  are  how  many  ? 

64.  31  — 1|  are  how  many  ? 

65.  4^  —  If  are  how  many  ? 

66.  5|  —  2|  are  how  many  ? 

67.  9|  —  7|  are  how  many  ? 

68.  2J  +  3J  — |  are  how  many  ? 

69.  4|  +  5f  —  2|  are  how  many  ? 

70.  3£  4-  4i  — J  are  how  many  ? 

71.  9|  -4-  3J  —  3  are  how  many  ? 

72.  a  -f  |  —  J  are  how  many  ? 

73.  |  4.  i  -f  ^.  —  i  are  how  many  ? 

74.  2|  are  how  many  times  fa  ? 

75.  31  are  how  many  times  -fa  ? 

76.  T\  are  how  many  times  ^\  ? 

77.  £  is  how  many  times  -^  ? 

78.  4  are  how  many  times  ^  ? 

79.  1}  are  how  many  times  T\  ? 

80.  J  are  how  many  times  -fj  ? 

81.  -jfij  are  how  many  times  ^  2 

82.  8|  are  how  many  times  2£  ? 

83.  10 J  are  how  many  times  T9j  ? 

84.  12£  are  how  many  times  1J  ? 

85.  j  +  i  4- 1  lacks  how  much  of  being  a  whole  one  ? 

86.  4  4-  |  +  f  lacks  how  much  of  being  a  whole 
one? 


90  ARITHMETIC. 

87.  A  lady  gave  £  of  all  her  money  for  a  dress,  ana 
f  of  it  for  a  shawl ;  what  part  of  her  money  had  she 
remaining  ? 

88.  £  of  an  army  was  killed,  and  •£  taken  prison 
ers  ;  what  part  of  the  army  escaped  ? 

89.  |  of  an  army  was  killed,  f  taken  prisoners,  and 
500  escaped  unhurt;  how  many  were  there  in  the 
army  ? 

90.  §  of  the  length  of  a  pole  is  in  the  ground,  £  in 
the  water,  and  12  feet  out  of  the  water ;  what  is  the 
length  of  the  pole  ? 

91.  A  market  woman  sold  |  of  all  her  oranges  to 
one  man  and  £  of  them  to  another,  and  then  had  only 
9   remaining;  how  many  had  she  at  first,  and  how 
many  did  she  sell  to  each  ? 

92.  A  man,  after  spending  £  of  his  fortune,  found 
that  $20  was  f  of  what  he  had  remaining ;  what  was 
his  fortune  ? 

93.  A  hawk  caught  f  of  Euphemia's  chickens,  a 
cat  killed  £  of  them,  and  \  of  them  died  ;  she  then  had 
13  remaining ;  how  many  had   she  at  first,  and  how 
many  were  destroyed  by  the  hawk  and  cat  respec 
tively  ? 

94.  Said  A  to  B  if  to  my  age  you  add  its  ^  and  -f , 
the  sum  will  be  38 ;  how  old  was  he  ? 

95.  A  is  40  years  old,  and  J-  of  his  age  is  -|  of  twice 
as  much  as  his  wife's  age  ;  how  old  was  his  wife  ? 


LESSON   XIV. 

REMARK. — By  inspecting  Lessons  8th  and  10th,  we  observe,  that  dividing 
both  Numerator  and  Denominator  by  the  same  number,  does  not  alter  the 
value  of  the  fraction.  Hence  to  reduce  a  fraction  to  its  lowest  terms,  we 
may  divide  both  numerator  and  denominator  by  any  number  that  is  con 
tained  in  each  of  them  without  a  remainder. 

1.  Reduce  f  to  its  lowest  terms. 

2.  Reduce  f  to  its  lowest  terms. 


ARITHMETIC 

3.  Reduce  f  to  its  lowest  terms. 

4.  Reduce  T5^  to  its  lowest  terms. 

5.  Reduce  T4¥  to  its  lowest  terms. 

6.  Reduce  if  to  its  lowest  terms. 

7.  Reduce  if  to  its  lowest  terms. 

8.  Reduce  &f  to  its  lowest  terms. 

9.  Reduce  f  f  to  its  lowest  terms. 

10.  Reduce  ff  to  its  lowest  terms. 

11.  Reduce  Jf  to  its  lowest  terms. 

12.  Reduce  T7/Q-  to  its  lowest  terms 

13.  .Reduce  |f  to  its  lowest  terms. 

14.  Reduce  4<M°  its  lowest  terms. 

15.  Reduce  ||  to  its  lowest  terms. 

16.  Why  does  the  value  of  the  fraction  remain  the 
same,  when  you  divide  both  numerator  and  denominator 
by  the  same  number  ? 

17.  When  you  rmiltiply  both  numerator  and  de- 
lominator   by    the    same    number,   why   does    it   not 
enange  the  value  of  the  fraction  ? 

18.  Reduce  4  times  |  to  its  lowest  terms. 

19.  Reduce  7  times  T4¥  to  its  lowest  terms. 

20.  Reduce  8  times  21  to  its  lowest  terms. 

21.  Reduce  6  times  -/T  to  its  lowest  terms. 

22.  Reduce  4  times  T5^  to  its  lowest  terms. 

23.  Reduce  12  times  -fj  to  its  lowest  terms. 

24.  Reduce  12  times  T5j  to  its  lowest  terms. 

25.  Reduce  8  times  ¥\  to  its  lowest  terms. 

26.  Reduce  7  times  -fj  to  its  lowest  terms. 

27.  Reduce  5  times  ij  to  its  lowest  terms. 

28.  Reduce  4  times  ^  to  its  lowest  terms. 

29.  Reduce  6  times  if  to  its  lowest  terms. 
SO.  rieduce  9  times  \ \  to  its  lowest  terms. 


ARITHMETIC, 


LESSON    XV. 

1.  If  3  ju  cut  an  apple  into  two  equal  pieces,  what 
will  1  of  these  pieces  be  called  ? 

2.  If  you  cut  £  of  an  apple  into  two  equal  pieces, 
*hat  part  of  a  whole  apple  will  1  of  these  pieces  be 
called  ? 

3.  If  Alice  has  1  of  a  lemon,  and  gives  \  of  it  to 
Ann,  what  part  of  a  lemon  will  Ann  receive  ? 

SOLUTION. — \  equals  f .     Therefore,  Ann  receives  £  ot 
J  of  a  lemon,  which  is  J  of  a  lemon. 

4.  George,  having  ^  of  a   melon,  gave  \  of  it  to 
Marcus ;  what  part  of  a  melon  did  he  receive  ? 

5.  Crary  had   |   of  a   dollar,  and   gave   \  of  it  to 
Joshua ;   what   part  of  a  dollar  did   Joshua   receive  ? 

6.  Robert  had  \  of  a  dollar,  and  gave  £  of  it  for  a 
cake ;  what  did  the  cake  cost  him  ? 

7.  Margaret  had  £  of  a  pound  of  candies,  and  Mary 
had  \  as  much  ;  how  much  had  Mary  ? 

8.  Jane  had  J  of  a  pound  of  sugar,  and  Ann  £  as 
much ;  how  much  had  she  ? 

9.  A   boy  bought   |  of  a  quart   of  chestnuts,  and 
gave  ^  of  them  to  his  sister ;   what  part  of  a  quart  did 
she  receive  ? 

10.  A  man  owned  \  of  a  share  in  a  bank,  and  sold 
\  of  that;  what  part  of  a  share  had  he  remaining  ? 

11.  B  owned  |  of  a  ship,  and  sold  \  of  his  share  \ 
what  part  of  a  whole  ship  did  he  sell  ? 

12.  What  is^ofi? 

13.  What  is  \  of£? 

14.  What  is  i  of  |? 

15  What  is  i  of  i? 

16  What  is  |  of  i? 

17  What  is  i  of  i? 

18.  What  U  4  of  Jl 

19.  What  is  |  of  Jt 


ARITHMETIC.  93 

20.  What  is  ^  of  £? 

21.  A  kite  was  up  in  the  air  and  fell  J  of  the  way 
to  the  ground,  it  then  arose  £  of  the  distance  it  lacked 
of  being  to  the  ground  ;  what  part  of  the  whole  distance 
was  it  above  the  ground  ? 

22.  Homer  is  J  as  old  as  his  father,  and  Nelson  is 
I  as  old  as  Homer ;  what  part  of  the  father's  age  is 
Nelson's  age  1 

23.  A  man,  owning  4  of  a  barrel  of  fish,  accom 
modated  his  neighbor  with  |  of  it ;  how  much  had  he 
remaining  ? 

24.  A  man,  having  \  of  an  eagle,  gave  }  of  it  to  B, 
and  B  gave  j\  of  what  he  had  to  C  ;  what  part  of  an 
eagle   had   each   after  this  division,   and   how  man} 
cents  had  each  ? 

25.  Elizabeth  had  |  of  a  pie,  and  gave  1  of  it  to 
Harriet ;  how  much  did  she  receive  ? 

SOLUTION. — %  of  }  is  J ;  and  if  £  of  J  is  £,  j  of  f  is  twice 
[,  which  are  f .     Therefore  Harriet  had  f  of  a  pie. 

26.  What  is  i  off? 

27.  What  is  i  of  |  ? 

28.  What  is  i  of  |  ? 

29.  What  is  i  of  f  ? 

30.  What  is  |  of  f  ? 

31.  What  is  |  of  f? 

32.  What  is  i  of  |  ? 

33.  What  is  i  of  A  ? 

34.  What  is]  of  |  ? 

35.  What  is  i  of  J  ? 

36.  What  isi  of  ^  ? 

37.  What  is  J  of  f  ? 

38.  What  is  ^  of  f  ? 

39.  What  is  }  of  If  . 

40.  What  is  |  of  Jl 


ARITHMETIC. 


41.  What  is  f  of  }  ? 

42.  What  is  f  of  4  ? 

43.  What  is  £  of  $? 

44.  What  is  f  of  4? 

45.  What  is  ^  of  £  ? 

46.  What  is  £  ofi? 

47.  What  is  £  of  J? 

48.  W^hat  is  f  of  i  ? 

49.  What  is  f  of  J  ? 

50.  What  is  ^  of  J? 

51.  What  is  |  of  a? 

52.  What  is  £  off? 

53.  What  is  |  off? 

54.  What  is  |  of  f  ? 

55.  What  is  |  of  f  ? 

56.  What  is  |  off? 

57.  What  is  |  of  -f  ? 

58.  What  is  4  of  £  ? 

59.  What  is  f  off? 

60.  What  is  T<L  of  |  ? 

61.  What  part  of  1  is  f  of  }  T 

62.  What  part  of  1  is  |  of  £  ? 

63.  What  part  of  2  is  |  of  1  ? 

64.  What  part  of  2  is  1  of  If  ? 

65.  WThat  part  of  2  is  f  of  1  ? 

66.  What  part  of  3  is  £  of  i  ? 

67.  What  part  of  4  is  1  of  14  ? 

68.  What  part  of  5  is  1  of  f  ? 

69.  What  part  of  9  is  ^  of  1 1  ? 

70.  What  part  of  2  is  f  of  f  ? 

71.  What  part  of  2  is  f  of  2J  ? 

72.  What  part  of  4  is  £  of  ^  ? 


ARITHMETIC.  05 

73.  What  part  of  6  is  f  of  f  ? 

74.  What  part  of  3  is  J  of  4f  ? 

75.  What  part  of  4  is  £  of  12f  ? 

76.  What  part  of  7  is  |  of  10 J  ? 

77.  Anthony  had  }  of  f  of  a  pound  of  cinnamon ; 
what  part  of  a  pound  had  he  ? 

78.  Albert  had  ^  of  f  of  a  quart  of  strawberries ; 
how  many  strawberries  had  he,  providing  1  quart  con- 
tained  42  strawberries  ? 

79.  Abner  gave  j  of  f  of  a  melon  to  his  brother ; 
what  part  of  a  melon  had  he  remaining  ? 

80.  Matilda  bought  f  of  a  quart  of  milk  for  tea,  and 
spilled  i  of  it ;  what  part  of  a  quart  had  she  remaining  ? 

81.  Edwin  picked  f  of  a  pail-full  of  blackberries, 
and  on  his  way  home  spilled  ^  of  them ;  what  part  of 
a  pail-full  had  he  remaining  ? 

82.  A  merchant  bought  f  of  a  hogshead  of  molasses, 
and  i  of  it  leaked  out ;  what  part  of  a  hogshead  had 
he  remaining  ? 

83.  Hannah  had  f  of  a  pound  of  candies,  and  gav 
}  of  them  to  Augusta ;  what  part  of  a  pound  did  she 
give  Augusta? 

84.  Elisha  found  $£  and  gave  £  of  it  to  Ephraim ; 
rhat  part  of  a  dollar  had  he  remaining  ? 

85.  Andrew  bought  f  of  a  pound  of  maple-sugar, 
nd  gave  |  of  it  to  Walter  ;  what  part  of  a  pound  did 
V  alter  receive  ? 

86.  Jacob,  having  a  pine-apple,  gave  2.  of  -^  of  it 
^  the  one  that  could  tell  how  much  that  would  be  ; 
'*ow  much  was  that  individual  to  receive  ? 

87.  James  gave  J  of  J  of  a  dime  for  a  top  •  what 
iid  the  top  cost  him  ? 

88.  Robert  gave  f  of  a  dollar  for  a  cap ;  what  did 
khe  cap  cost  him  ? 

89.  Mary  gave  1  of  1 J  dimes  for  a  comb ;  what 
did  the  comb  cost  her  ? 


96  ARITHMETIC. 

90.  Clorinda  gave  |  of  6  dimes  for  a  pair  of  gloves  j 
how  much  did  the  gloves  cost  her  ? 

91.  A  man,  having  4J  barrels  of  flour,  sold  |  of  it; 
how  much  remained  unsold  ? 

92.  A  man  gave  f  of  $3 J  for  a  silver  pencil ;  what 
was  the  cost  of  the  pencil  ? 

93.  Jane  worked  8J  hours  in  a  day,  and  Delilah 
worked  only  £  as  many ;   how  many  hours  did  she 
work  in  a  day  ? 

94.  B  gave  $32f  for  a  cow,  which  was  |  as  much 
as  A  gave  for  his ;  what  did  A's  cow  cost  him  ? 

95  Darius  is  18  J  years  old,  and  Daniel  is  J  as  old ; 
how  old  is  he  ? 

96.  If  1  yard  of  cloth  cost  $5J,  what  will  f  of  a 
yard  cost  ? 

97.  If  4  yards  of  cloth  cost  $9£,  what  will  J  of  a 
yard  cost  ? 

98.  If  5  barrels  of  beef  cost  $18£,  what  will  £  of  a 
barrel  cost  ? 

99.  If  |  of  an  apple  cost  J  of  a  cent,  what  will  ] 
apple  cost. 

100.  If  £  of  an  orange  cost  1£  cents,  what  will  ^ 
of  an  orange  cost  ? 

101.  If  5  pounds  of  butter  cost  6J  dimes,  how  many 
cents  will  If  pounds  cost  ? 


LESSON    XVI. 

1.  If  4  barrels  of  flour  cost  $14|,  what  will  f  of  a 
barrel  cost  ? 

2.  If  3  bushels  of  potatoes  cost  5}  dimes,  what  will 
1£  bushels  cost  ? 

3.  If  21  bushels  of  apples  cost  6£  dimes,  how  many 
cents  will  f  of  a  bushel  cost  ? 

4.  If  |  of  an  apple  cost  |  of  a  cent,  what  will  1 
apple  cost  ? 


ARITHMETIC.  97 

5.  If  f  of  an  orange  cost  f  of  a  cent,  what  will  j 
of  an  orange  cost  ? 

6.  If  2J  yards  of  cassimere  cost  $3|,  what  will  5J 
yards  cost  ? 

7.  If  5|  yards  of  shalloon  cost  $5T^,  what  will  2 
yards  cost  ? 

8.  If  in  34  hours  A  can  do  a  certain  piece  of  work, 
how  long  will  it  take  him  to  do  a  piece  of  work  If 
times  as  large  ? 

9.  f  of  A's  age  is  f  of  B's ;  and  J  of  B's  age  is  f 
of  C's  age.     How  old  are  A  and  B  respectively,  pro- 
viding  C  is  81  years  old  ? 

10.  Bought  3|  boxes  of  goods,  at  $6T6Tv  a  box,  and 
paid  for  it  with  sheep,  at  $2  a  head ;  how  many  sheep 
did  it  take  ? 

11.  How  many  times  |  is  J  ? 

SOLUTION. — 1  is  contained  in  f ,  f  times ;  and,  if  1  rs 
contained  in  f ,  J  times,  }  is  contained  in  J  5  times  f  times, 
which  are  \a  times,  and  f  is  contained,  ^  of  \5  times,  which 
is  y  times. 

12.  How  many  times  |  is  J  \ 

13.  How  many  times  |  is  \  ? 

14.  How  many  times  f  is  ^  ? 

15.  How  many  times  f  is  T3F  ? 

16.  How  many  times  |  is  \\  ? 

17.  How  many  times  f  is  T4T  ? 

18.  How  many  times  |  is  -J  '? 

19.  How  many  times  J  is  3^  ? 

20.  How  many  times  f  is  2|  ? 

21.  How  many  times  |  is  2f  ? 

22.  How  many  times  f  is  5£  ? 

23.  How  many  times  |  is  T3¥  ? 

24.  How  many  times  |  is  i-J  ? 

25.  How  many  times  f  is  31  ? 

26.  How  many  times  J  is  4|  ? 


98  ARITHMETIC. 

27.  How  many  times  1  £  is  2|  ? 

28.  How  many  times  2f  is  1]  ? 

29.  How  many  times  *3£  is  5£  ? 

30.  How  many  times  4|  is  5|  ? 

31.  A  farmer  sold  a  quantity  of  rye  for  $96,  which 
was  only  J  of  what  it  was  worth ;  how  much  did  he 
lose  by  the  bargain  ? 

32.  A  man  sold  a  cow  for  If  times  what  she  cost 
him,  and  by  so  doing  gained  $6  ;   what  did  the  cow 
cost  him  ? 

33.  A  merchant  sold  a  quantity  of  goods  for  }£  of 
what  they  cost,  and  by  so  doing,  he  lost  $15 ;  what 
did  the  goods  cost  him  ? 

34.  A  farmer,  having  lost  12  sheep,  found,  that  only 
J  of  his  flock  remained ;   how  many  sheep  had  he 
remaining  ? 

35.  An  individual,  being  asked  how  many  geese  ne 
had,  answered,  that  if  to  ^  of  his  flock  24  geese  were 
added,  the  sum  would  equal   If  times  his  original 
flock  ;  how  many  geese  had  he  ? 

36.  If  |  of  a  yard  of  cloth  cost  $f ,  what  will  f  of  a 
yard  cost } 

37.  A  boy,  being  asked  his  age,  said,  that  8J  years 
was  f  of  twice  as  much  as  his  age  ;  how  old  was  he  ? 

38.  If  |  of  the  candies  I  have  cost  7£  cents,  what 
will  I  of  them  cost  ? 

39.  What  will  f  of  a  barrel  of  flour  ;ost,  if  4  of  a 
barrel  cost  $2j  ? 

40.  What  will  |  of  an  orange  cost,  if  $  of  an  orange 
cost  2J-  cents  ? 

41.  How  many  yards  of  cloth  will  be  required  to 
make  a  coat,  if  1|  yards  will  make  |  of  a  coat  ? 

42.  f  of  2  are  how  many  times  |  ? 

43.  -ft  of  8  are  how  many  times  |  ? 

44.  |  of  7  are  how  many  times  3  ? 

45.  }  of  8  are  how  many  times  f  ? 


ARITHMETIC.  99 

-,.>  .  .    . 

46.  f  of  12  are  how  many  times  |  of  6 

47.  f  of  7  are  how  many  times  J  of  2  ? 

48.  If  f  of  3  yards  of  cloth  cost  $1},  what  will  } 
of  7  yards  cost  ? 

49.  If  4  of  6  yards  of  cloth  cost  $2^,  how  much 
will  |  of  7  yards  cost  ? 

50.  If  f  of  f  of  a  barrel  of  flour  cost  $lf ,  what  will 
J  of  £  of  J  of  a  barrel  cost  ? 


LESSON    XVII. 

1.  12  is  £  of  what  number  ? 

SOLUTION. — If  12  is  J  of  some  number,  J  of  that  number 
is  ^  of  12,  which  is  4  ;  if  4  is  £  of  that  number,  }  (which  in 
that  number)  is  4  times  4,  which  are  16.  Therefore  12  is 
J  of  16. 

2.  15  is  |  of  what  number  ? 

3.  18  is  f  of  what  number? 

4.  20  is  j-  of  what  number  ? 

5.  26  is  |  of  what  number  ? 

6.  25  is  ^  of  what  number? 

7.  30  is  f  of  what  number  ? 

8.  32  is  f  of  what  number  ? 

9.  36  is  ^  of  what  number  ? 

10.  36  is  ^  of  what  number  ? 

11.  36  is  f  of  what  number? 

12.  24  is  Jf  of  what  number  ? 

13.  9  is  ^  of  what  number  ? 

14.  12  is  f  of  what  number  ? 

15.  38  is  |  of  what  number  ? 

16.  16  is  £  of  what  number? 

17.  16  is  |  of  what  number  ? 

18.  16  is  |  of  wj-  at  number  ? 


100  ARITHMETIC. 


19.  40  is  |  of  what  number  ? 

20.  40  is  f  of  what  number? 

21.  72  is  |  of  what  number  ? 

22.  72  is  ft  of  what  number  ? 

23.  12  is  |  of  how  many  times  2  ? 

24.  16  is  £  of  how  many  times  3  ? 

25.  18  is  |  of  how  many  times  9  ? 

26.  32  is  4  of  how  many  times  4? 

27.  46  is  |  of  how  many  times  23  ? 

28.  48  is  f  of  how  many  times  5  ? 

29.  48  is  -|  of  how  many  times  4  ? 

30.  36  is  -|  of  how  many  times  2  ? 

Q1     30  is  |  of  how  many  times  £  of  12  ? 

30  is  ^  of  how  many  times  ^  of  10  ? 

16  is  f  of  how  many  times  |  of  9  ? 

16  is  ft  of  how  many  times  J  of  16  ? 

24  is  f  of  how  many  times  f  of  12  ? 
so.  25  is  £  of  how  many  times  ±  of  9  ? 

37.  35  is  ft  of  how  many  times  |  of  9  ? 

38.  40  is  f  of  how  many  times  £  of  10  ? 
2Q    48  is  j\  of  how  many  times  |  of  25  ? 

96  is  |  of  how  many  times  J  of  16  ? 


31 
32 

33 
34 
35 
36 


39 
40 


LESSON    XVIII. 

1.  |  of  6  is  |  of  what  number  ? 

2.  |  of  10  is  |  of  what  number  ? 

3.  |  of  8  rs  f  of  what  number  ? 

4.  f  of  21  is  f  of  what  number? 

5.  A  of  15  is  T\  of  what  number  ? 

6.  T\  of  40  is  f  ©f  what  number? 


ARITHMETIC.  101 


7.  |  of  27  is  |  of  what  number  ? 

8.  |  of  27  is  T8T  of  what  number  ? 

9.  f  of  81  is  y°7  of  what  number? 

10.  %  of  49  is  T6T  of  what  number  ? 

11.  |  of  12  is  i  of  how  many  times  2  ? 

12.  £  of  16  is  |  of  how  many  times  2  ? 

13.  |  of  10  is  f  of  how  many  times  4  ? 

14.  J  of  16  is  -^j  of  how  many  times  6  ? 

15.  |  of  15  is  f  of  how  many  times  6  ? 

16.  f  of  20  is  |  of  how  many  times  3  ? 

17.  f  of  12  is  f  of  how  many  times  5  ? 

18.  f  of  20  is  £  of  how  many  times  3  ? 

19.  J  of  36  is  yi  of  how  many  times  4  ? 

20.  f  of  72  is  |  of  how  many  times  12  ? 

21.  f  of  96  is  f  of  how  many  times  90  ? 

22.  £  of  117  is  J  of  how  many  times  4  ? 

23.  -^  of  56  is  f  of  how  many  times  8  ? 

24.  |  of  60  is  |  of  how  many  times  5  ? 

25.  |  of  36  is  |  of  how  many  times  12  ? 
*tQ.  J  of  72  is  f  of  how  many  times  5  ? 

27.  f  of  40  is  T5j  of  how  many  times  21  f 

28.  f  of  32  is  |  of  how  many  times  9  ? 

29.  2.  of  15  is  4  of  how  many  times  2  ? 

30.  |  of  15  is  i  of  how  many  times  9  ? 

31 .  |  of  24  is  f  of  how  many  times  a  ? 

32.  £  of  45  is  £  of  how  many  times  3  ? 

33.  4  °f  14  is  |  of  how  many  times  5  ? 

34.  j  of  18  is  |  of  how  many  times  7  ? 

35.  y\  of  40  is  f  of  how  many  times  6  I 

36.  |  of  45  is  T6T  of  how  many  times  3  ? 

37.  ^  of  35  is  f  of  how  many  times  2  ? 

38.  J  of  81  is  A  of  how  many  times  9  ? 


102 


ARITHMETIC. 


39.  |  of  5  is  §  of  how  many  times  7  ? 

40.  J  of  7  is  |  of  how  many  times  3  ? 

41.  B's  horse  cost  $60,  and  f  of  the   cost  of  the 
horse,  is  J  of  two  times  the  value  of  his  wagon  ;  what 
is  the  value  of  his  wagon  ? 

42.  A  coat  cost  $20,  and  £•  of  the  cost  of  the  coat, 
is  f  of  8  times  the  price  of  a  hat ;  the  price  of  the 
hat  is  required. 

43.  If  a  cow  cost  $30,  and  f  Of  this,  is  S  of  10  timea 
the  price  of  a  sheep  ;  what  is  the  price  of  a  sheep  ? 

44.  A's  farm  is  worth    $1200,  and  J  of  its  value, 
is  £  of  10  times  the  value  of  its  yearly  productions ; 
what  is  the  value  of  the  yearly  productions  ? 

45.  The  articles  contained  in  a  certain  store  cost 
$500,  and  T3^-  of  their  cost,  is  |  of  3  times  the  amount 
paid  for  the  silks ;  what  did  the  silks  cost,  and  what 
the  other  articles  ? 

46.  A's  wedding  clothes  cost  $180,  and  |  of  the 
cost  of  his  clothes,  is  f  of  6  times  the  cost  of  his  wife's 
Wedding  dress  ;  what  was  the  cost  of  her  dress  ? 

47.  The  insurance  of  a  ship  amounted  to  $800,  and 
[  of  that  is  -jV  of  2  times  the  value  of  the  cargo ;  what 
is  the  value  of  the  cargo? 

48.  A's  house  cost  $1400,  and  J  of  its  cost,  is  3* 
times  \  of  the  cost  of  the  furniture  contained  in  it ; 
what  was  the  cost  of  the  furniture  ? 

49.  Providing  a  house  was  worth  $1200,  and  f  of 
its  value  was  f  of  ^  times  the  value  of  the  farm  on 
which  it  stood ;  what  was  the  value  of  the  farm  ? 

50.  If  a  sleigh  cost  $100,  what  would  be  the  cost 
of  a  wagon,  if  |  of  the  cost  of  the  sleigh  was  /T  of 
twice  the  cost  of  a  wagon  ? 

51.  Lambert  is  worth  $2500,  and  f  of  his  fortune, 
is  3£  times  £  of  Latham's  fortune ;    how  much  ia 
Latham  worth? 

Distances  on  the  Railroad  between  Albany  and  Buffalo 

52.  The  distance  from  A.bany  to  Schenectady,  ia 


ARITHMETIC.  103 

16  miles,  and  f  of  this  distance,  is  $  of  J-  times  the 
distance  from  Albany  to  Rome ;  what  is  the  distance 
to  Rome? 

53.  Fort-Plain  is  56  miles  from  Albany,  and  ^  of 
this  distance  is  1|  times  T\  of  the  distance  from  Albany 
to  Rochester ;  what  is  the  distance  to  Rochester  ? 

54.  Waterloo  is  192  miles  from  Albany,  and  £  of 
this  distance  is  If  times  the  distance  to  Utica,  and  3 
miles  more  ;  what  is  the  distance  to  Utica  ? 

55.  Buffalo  is  325  miles  from  Albany,  and  f  of  this 
distance  is  71  times  -JT  of  the  distance  to  Batavia,  and 
5  miles  more ;  what  is  the  distance  to  Batavia  ? 

Distances  on  the  Railroad  between  Albany  and  Boston. 

56.  Boston  is  200  miles  from  Albany,  and  f  of  this 
distance,  is  1J  times  -J  of  the  distance  to  West  Spring 
field  ;  what  is  the  distance  to  West  Springfield  ? 

57.  From  Albany  to  the  state  line  is  38  miles,  and 
1£  times  this  distance,  is  4|   times  £  of  the  distance 
to  Wilbraham ;  what  is  the  distance  to  Wilbraham  ? 

58.  Kinderhook  is  16  miles  from  Albany,  and  f  ot 
this  distance,  is  J  times  i  of  the  distance  to  Dalton ; 
what  is  the  distance  to  Dalton  ? 

59.  Brighton  is  195  miles  from  Albany,  and  J  of 
this  distance  is  J  of  2  times  the  distance  to  Worces 
ter  ;  what  is  the  distance  to  Worcester  ? 

60.  Grafton  is  162  miles  from  Albany,  and  J-  of  this 
distance  is  %  of  3  times  the  distance  to  Westiield, 
lacking  2  miles  ;  how  far  is  it  to  Westfield  1 


LESSON    XIX. 


104  ARITHMETIC. 


5.  f  of  36  is  £  of  how  many  times  f  of  12  ? 

6.  f  of  45  is  $  of  how  many  times  f  of  14  ? 

7.  |  of  80  is  |  of  how  many  times  £  of  10  ? 

8.  -}-£  of  48  is  £  of  how  many  times  -f  of  7  ? 

9.  J  of  45  is  |  of  how  many  times  f  of  8  ? 

10.  4  °f  35  is  J  of  how  many  times  -f  of llf  ? 

11.  J  of  54  is  ^  of  how  many  times  J  of  10£? 

12.  J  of  25  is  f  of  how  many  times  f  of  10  ? 

13.  4  of  28  is  |  of  how  many  times  |  of  25  ? 

14.  £  of  18  is  |  of  how  many  times  f  of  12  ? 

15.  f  of  36  is  |  of  how  many  times  |  of  12  ? 

16.  f  of  54  is  |  of  how  many  times  |  of  16  ? 

17.  J  of  32  is  |  of  how  many  times  f  of  9  ? 

18.  f  of  108  is  |  of  how  many  times  |  of  f  of  15  ? 

19.  f  of  40  is  -fj  of  how  many  times  ^  of  f  of  20? 

20.  |  of  20  is  |  of  how  many  times  f  of  £  of  12  ? 


LESSON    XX. 

1.  If  1  horse  eat  J  of  a  bushel  of  oats  in  1  day, 
how  many  horses  will  eat  a  bushel  in  the  same  time? 

2.  If  the  wages  of  8  weeks  amount  to  $48,  what 
will  the  wages  of  2 J  weeKs  amount  to  ? 

3.  A  ship's  crew  of  12  men  have  provision  for  5 
months ;  how  many  months  would  it  last  5  men  ? 

4.  A  man  gained  $14  by  selling  a  watch  for  1§ 
times  what  it  cost  him ;  how  much  did  it  cost  him  ? 

5.  There  is  a  pole,  £  of  its  length  is  under  water, 
and  9  feet  out ;  how  long  is  the  pole  ? 

6.  A  pole  is  standing  in  the  water,  so  that  15  feet 
is  above  the  water,  which  is  ^  of  the  whole  length  t>f 
the  pole ;  how  long  is  the  pole  ? 

7.  J  is  |  of  what  number  ? 


AEITHMETIC.  l06 

8.  If  8    horses  can    in   1   day  eat  4  bushels  of 
oats,  how  many  days  would  it  take  1  horse  to  eat  1 
bushel  ? 

9.  If  3  horses  can  in  1  day  eat  If  bushels  of  oats, 
how  many  bushels  can  1  horse  eat  in  4  days  ? 

10.  If  1  horse  in  2  days  can  eat  6  bushels  of  corn, 
how  many  bushels  will  4  horses  eat  in  3  days  ? 

11.  If  4  horses  eat  16  bushels  of  provender  in  2 
lays,  how  many  bushels  will    3   horses  eat  in   12 
4ays. 

12.  How  many  tons  of  hay  Will  3  horses  consume 
in  4  days,  if  4  horses  will  in  £  of  a  day  consume  J  of 
a  ton? 

13.  How  many  hundred  weight  of  hay  can  3  horses 
consume  in  25  days,  if  2  horses  in  J  of  a  day  con 
sumed  TJ0-  °f  a  hundred  weight  ? 

14.  How  many  days  would  it  require,  for  4  men 
to  cut  16  cords  of  wood,  if  1  man  in  1  day  cut  £  of  a 
cord? 

15.  How   many    men  will    be   required,  to   earn 
20  dimes  in  4  days,  if  4  men  in  2£  days  earn  11 
dimes  ? 

16.  If  it  require  6  days  for  2  men  to  lay  36  rods 
of  wall,  how  many  men  can  in  £  of  the  time  build 
72  rods  of  similar  wall  ? 

17.  If  in  4  days  3  men  accomplish  a  certain  piece 
of  work,  how  many  men  will  be  required,  to  perform 
a  piece  of  work  4  times  as  large  in  2  days  ? 

18.  If  4  men  in  8  days  perform  a  certain  piece  off 
work,  how  many  men  will  be  necessary  to  accom 
plish  3  times  as  much  work  in  J  of  a  day  ? 

19.  If  1   horse  eat  1  bushel  of  oats  in  4  days,  in 
how  many  days  would  6  horses  eat  48  bushels  ? 

20.  If  2  men  in  1  of  a  day  earn  T5T  of  a  dollar, 
how  many  days  would  it  take  3  men  to  earn  f  of  a 
dollar? 

21.  If  it  require  J  of  a  bushel  of  oats  to  feed  4 


106  ARITHMETIC. 

horses  1  of  a  day,  how  many  horses  would  it  take  to 
consume  9  bushels  in  j  of  a  day  ? 

0^7"  SUGGESTION. — Review  unless  the  pupils   thor 
oughly  understand  the  preceding  Chapters. 


CHAPTER    VII. 
LESSON    I. 

1.  $24  is  |  of  twice  as  much  as  a  cask  of  wine* 
cost ;  what  did  the  wine  cost  ? 

2.  Bought  30  barrels  of  flour,  and  f  of  the  number 
of  barrels,  equaled  1  as  many  dollars  as  they  all  cost ; 
what  did  1  barrel  cost  ? 

3.  35  is  |  of  how  many  times  |  of  4  ? 

4.  A  farmer,  being  asked  how  many  sheep  he  had, 
answered,  that  160  was  |  of  10  times  his  number  ; 
now  many  sheep  had  he  ? 

5.  Mr.  B,  being  asked  the  value  of  his  horse,  said, 
that  $54  was  T6T  of  3  times  its  value  ;  what  was  the 
value  of  his  horse  ? 

6.  72  is  f  of  how  many  times  f  of  12  ? 

7.  36  is  £  of  how  many  times  f  of  12  ? 

8.  48  is  |-  of  how  many  times  ^  of  18  ? 

9.  56  is  |  of  how  many  times  £  of  8  ? 

10.  60  is  j  of  how  many  times  f  of  16  ? 

11.  84  is  l-/  of  how  many  times  -J  of  25  ? 

12.  A  spent  $60,  which  was  |  of  4  times  as  muc!> 
as  he  was  worth ;  how  much  was  he  worth  ? 

13.  B  sold  9  sheep,  which  was  T%-  times  ^  of  hia 
wl^le  flock ;  how  many  sheep  had  he  remaining  ? 

1'J.  D,  at  a  game  of  cards,  lost  $20,  which  was  ^ 

times  ^  of  all  the  money  he  had ;  how  much  had  he  ? 

15.  C  found  $45,  which  was  f  of  3  times  as  much 


ARITHMETIC.  107 

as  he  already  had ;  how  much  more  did  he  find  than 
he  had  at  first? 

16.  A  boy  lost  9  marbles,  which  was   f  of  twice 
as  many  as  he  had  at  first ;  how  many  had  he  remain 
ing? 

17.  A  boy  gave  away  8  apples,  which  was  f    of 
twice  as  many  as  he  then  had ;  how  many  had  he  a 
first? 

IS.   12  is  |  times  -f  of  what  number  ? 

19.  36  is  T6T  times  f  of  what  number  ? 

20.  Jeremiah  is  18  years  old,  and  his  age  is  f  times 
|  of  his  father's  age  ;  how  old  is  his  father  ? 

21.  Mary  gave  6   cents   for  a  comb,  which  was  f 
times  ^  of  all  the  cents  she  had  ;  how  many  cents  had 
she  ? 

22.  Martha  gave   8   cents  for  a  pine-apple,  which 
was  f   times   f    of  all    her  money;  how  many  apples 
could  she  have  bought  wi^h  the  money  she  had  remain 
ing,  at  2  cents  apiece  ? 

23.  Henry  had  20  marbles,  which  was  |  of  twice  as 
many  as  Harry  had ;  how  many  had  Harry  ? 

24.  Margaret  is  16  years  old,  and  her  age  is  f  of  3 
times  Martha's  age;  how  old  is  Martha  ? 

25.  |  is  f  of  twice  as  much  as  what  number  1 

26.  A  man  bought  a  horse  for  $60,  which  was  %  of 
twice  as  much  as  he  sold  him  for;  how  much  did  he 
gain  by  the  bargain  ? 

27.  A  horse  was  sold  for  $40,  which  was  J  times 
|  of  what  he  was  worth;  what  was  the  Value  of  the 
horse  ? 

28.  A  man,  when  he  was  married,  was  20   years  of 
age,  which  was  f  times  f  of  the  age  of  his  wife  ;  how 
old  was  she  ? 

29.  Shepherd  was  worth  $160,  which  was  -f  times 
TV    of   his    father's   fortune  ;    what  was  the    father's 
fortune  ? 

30.  A  and  B  were  playing  cards,  B  lost  $14  which 


108  ARITHMETIC. 

was  T\  times  |  as  much  as  A  then  had  ;  and  when 
they  commenced  £  of  A's  money  equaled  $  of  B's. 
How  much  had  each  when  they  began  to  play  ? 


LESSON    II. 

1.  A   boy,    after   spending   J   of  all    his   money, 
found,  that  16  cents  was  all  he  had  remaining  ;  how 
much  had  he  at  first  ? 

SOLUTION. — Let  f  equal  all  he  had  at  first.  Then  after 
spending  f  of  it,  he  must  have  had  remaining  f —  f,  which 
is  §.  And  this  by  the  condition  of  the  question  is  16 
cents.  If  16  cents  is  f  of  what  he  had  at  first,  j  of  what 
he  had,  is  \  of  16  cents,  which  is  8  cents;  and  |  (what  he 
had  at  first)  is  5  times  8  cents,  which  are  40  cents. 

2.  Ruth,  after  losing  f  of  all  her  roses,  had  only  3 
remaining  ;  how  many  had  sfre  at  first  ? 

3.  Jane  gave  J  of  all  her  flowers  to  Ann,  and  had 
4  remaining  ;  how  many  did  she  give  to  Ann  ? 

4.  George,  after  eating  -^  of  all  his  oranges,  found 
that  8  oranges  were  all  he  had  remaining  ;  how  many 
had  he  at  first  ? 

5.  A  boy  expended  £  of  his  money  for  a  pie,  f  for 
a  ball,  |  for  a  top,  and  had  6  cents  remaining  ;  how 
many  cents  had  he  at  first  ? 

6.  In  a  certain  school  £  of  the  scholars  study  gram 
mar,  i  study  arithmetic,  and  the  remainder,  which  is 
10,  study  geography  ;  how  many  scholars  in  all,  and 
how  many  attending  to  each  study  ? 

7.  A  third  part  of  an  army  was  killed,  J  part  taken 
prisoners,    and    300    remained    unhurt ;    how    many 
were  there  in  the  army  ? 

8.  If  from  my  age  you  subtract  i  and  f  of  my  age, 
the  remainder  would  be  2  years  ;  how  old  am  1  ? 

9.  B,  being  asked  how  many  pigeons  he  caught, 
said,  that  if  to  4  of  the  number,  36  were  added,  tha 


ARITHMETIC.  109 

gum  would  equal  twice  the  number.     How  many  did 
he  catch  ? 

10.  If  to  J  of  the  cost  of  B's  horse  you  add  $100, 
the  sum  will  be  twice  the  cost  of  the  horse  ;  what  was 
the  cost  of  the  horse  ? 

11.  A  gentleman,  after  spending  $  of  his  fortune 
and  J  of  the  remainder,  had  $2400  remaining ;  what 
was  his  fortune  ? 

12.  A  gambler  lost  J  of  all  his  money,  and  the 
next  night  he  won  f  as  much  as  he  lost  the  night  be- 
fore ;  he  then  had  $90  :  how  much  had  he  at  first  ? 

13.  A  man  willed  |  of  his  fortune  to  his  wife,  $  to 
his  son,  i  to  his  daughter,  and  the  remaining  $200  he 
bestowed  for  charitable  purposes.     What  was  his  for 
tune,  and  what  did  he  will  to  each  ? 

14.  A  traveler  had  stolen  from  him  -|  of  all  his 
money  ;   the  thief  was  caught,  but  not  until  he  had 
snent  £  of  it,  the  remainder  ($100)  was  given  back ; 
how  rir'ch  had  he  at  first  ? 

15.  If  to  i  of  the  cost  of  A's  watch  you  add  $10, 
the  sum  will  be  $21 ;  what  was  the  cost  of  his  watch  ? 

16.  If  to  |  of  B's  age  you  add  7  years,  the  sum 
would  be  39  years ;  how  old  is  B  ? 

17.  A  drover,  being  asked  how  many  sheep  he 
had,  said,  if  to  £  of  my  flock  you  add  the  number  9£, 
the  sum  will  be  99£  ;  how  many  sheep  had  he  ? 

18.  ^  of  the  length  of  a  pole  is  in  the  water,  and  12 
reet  in  the  air ;  how  long  is  the  pole  ? 

19.  If  to  J  of  A's  age  you  add  16  years,  the  sum 
will  be  1|  times  his  age ;  how  old  is  he  ? 

20.  A   man,   being  asked  how  many  pigeons  he 
caught,  replied,  that  if  to  f  of  the  number  he  caught 
you  add  20,  the  sum  lacking  4  would  be  1£  times  the 
number  ;    how  many  did  he  catch? 


110  ARITHMETIC. 


LESSON    III 

1.  Divide  the  number  36  into  two  parts,  whicn  shall 
be  to  each  other  as  7  to  2. 

SOLUTION. — Since  the  two  parts  are  to  be  to  each  other 
as  7  to  2,  we  must  divide  36  into  7  +  2,  which  are  9  equal 
parts ;  and  7  of  the  parts  will  be  one  of  the  numbers,  and 
2  of  them  the  other.  £  of  36  is  4,  and  J  is  7  times  4,  which 
are  28  (the  first  number,)  and  f  is  2  times  4,  which  are  8 
(the  other  number.) 

2.  Two  men  hired  a  pasture  for  $72 ;  one  put  in  7 
horses,  and  the  other  2  horses ;  what  ought  each  to  pay  ? 

3.  A  and  B  hired  a  pasture  for  $14;   A  put  in  4 
cows,  and  B  put  in  3  cows ;  what  ought  each  to  pay  ? 

4.  A  and  B  bought  a  lottery  ticket  for  $5 ;  A  paid 
$3,  and  B  paid  $2.     They  drew  a  prize  of  $60  ;  what 
was  each  one's  share  ? 

5.  Two  men  bought  40  mules  ;  the  first  paid  $5  as 
often  as  the  other  $3.     How  many  mules  ougiu  each 
to  receive  ? 

6.  Mary  and  Elizabeth  went  to  school  80  days,  and 
as  often  as  Mary  went  3  days,  Elizabeth  went  5  days ; 
how  many  days  did  each  go  ? 

7.  Ruben  had  7  cents,  and  Blake  4  cents ;    they 
paid  all  their  money  for  22  apples ;  how  many  ought 
each  to  receive  ? 

8.  Three  men  bought  a  lottery  ticket  for  $12  ;  the 
first  paid  $2,  the  second  $7,  and  the  third  $3.     They 
drew  a  prize  Of  $240 ;  what  was  each  man's  share  ? 

1  9.  Three  men  hired  a  pasture  for  $24  ;  the  first  pul 
in  2  horses,  the  second  put  in  3  horses,  and  the  3d  put 
in  4  horses ;  what  ought  each  to  pay  ? 

10.  A  man,  failing  in  business,  was  able  to  p&y 
only  A  of  his  debts ;   what  will  that  man  receive  io 
whom  he  owes  $90  ? 

11.  A  man,  meeting  an  equal  number  of  poor  wo 


ARITHMETIC.  Ill 

men  and  boys,  gave  to  each  woman  7  dimes,  and  to 
each  boy  2  dimes ;  and  to  them  all  he  gave  $9 :  how 
many  women  and  boys  were  there  respectively  ? 

12.  Two  men  bought  a  barrel  of  fish  for  $9 ;   the 
first  paid  $4,  the  second  $5 ;  what  part  of  the  barrel 
belongs  to  each  ? 

13.  A  farmer  gave  35  bushels  of  rye  to  2  of  his 
poor  neighbors  ;   to  the  first  he  gave  1  bushel  as  often 
as  to  the  other  J  of  a  bushel :  how  many  bushels  did 
each  receive? 

14.  Three  men  hired  a  pasture  for  $36 ;  the  first 
put  in  3  horses,  the  second  2  horses,  and  the  third  4 
horses ;  how  much  ought  each  to  pay  ? 

15.  Two  men  hired  a  pasture  for  $60 ;  the  first 
put  in  4  horses  for  2  weeks,  and  the  second  put  in  3 
horses  for  4  weeks.     What  ought  each  to  pay  ? 

16.  Three  men  hired  a  pasture  for  $15  ;  the  first 
put  in  4  sheep  for  5  weeks,  the  second  put  in  8  sheep 
for  5  weeks,  and  the  third  put  in  10  sheep  for  9  weeks. 
What  ought  each  to  pay  ? 

17.  Two  men  entered  into  partnership ;  the  first 
put  in  $40  for  10  months  and  the  second  put  in  $80 
for  5  months ;  they  gained  $95  :  what  was  each  man's 
share  of  the  gain  ? 

18.  A  and  B  agreed  to  cut  a  field  of  wheat  for 
$20 ;  A  sent  5  men  for  4  days,  and  B  sent  3  men  for 
10  days;    what  ought  A   and  B  to  receive  respec 
tively  ? 

19.  Divide  $56  between  A  and  B,  giving  to  A  $1 
as  often  as  f  of  a  dollar  to  B. 

20.  A  and  B  hired  a  pasture  for  $24 ;   A  put  in  4 
sheep  for  10  weeks,  and  B  put  in  2  horses  for  10 
weeks ;  what  ought  each  to  pay,  providing  2  sheep 
in     week  eat  as  much  as  a  horse  in  the  same  time  ? 


112  ARITHMETIC. 


LESSON    IV. 

1 .  B  had  4  apples  more  than  A,  and  they  together 
had  14  ;  how  many  had  each  ? 


B 

eq< 
ber,  &c. 

2.  Heman  has  6  books  more  than  Handford,   and 
they  together  have  26  ;  how  many  has  each  ? 

3.  Robert  has  7  marbles  more  than  Richard,  and 
they  together  have  35 ;  how  many  has  each  ? 

4.  Mary  has  4  roses  more  than  Martha,  and  they 
together  have  24  ;  how  many  has  each  ? 

5.  Alice  has  7  pins  more  than  Abner,  and  they  to 
gether  have  29  ;  how  many  has  each  ? 

6.  |  of  |  is  |  of  what  number  ? 

7.  The  sum  of  two  numbers  is  36,  and  their  differ, 
ence  is  16  ;  what  are  the  two  numbers  ? 

8.  A  boy  bought  ^  of  a  melon  for  8^  cents ;  how 
much  is  that  apiece  ? 

9.  Homer  and  Hannah  each  bought  an  equal  num. 
ber  of  peaches ;  on  their  way  home  Hannah  had  4 
more  given  to  her,  then  they  together  had  24 :  how 
many  did  each  buy  1 

10.  Two  boys  had  each  an  equal  number  of  blocks  ; 
one  lost  4  of  his  ;  and  they  together  then  had  only  12 
remaining  :  how  many  had  each  at  first  ? 

11.  A  wagon  was  sold  for  $17|,  which  was  |  aa 
much  as  it  cost ;  what  did  it  cost  ? 

12.  Hiram    had    twice  as  many  strawberries   a? 
Eugene,  and  they  together  had  18  pints ;  how  many 
had  each  ? 

13.  Joshua  had  6  cents  more  than  twice  as  many 
as  Jordon,  and  they  together  had  36  ;  how  many  had 
each  ? 

14.  Susan  had  \  as  many  cents  as  Sarah ;  Sarah 


ARITHMETIC.  113 

lost   10  of  hers ;  then  they  together  had  50 ; — how 
many  had  each  at  first  ? 

15.  Thomaf  was  returning  from  market  with  twice 
as  many  eggs  as  Timothy ;  Thomas  broke  4  of  his, 
and  Timothy,  6  of  his ;  they  then  together  had  only 
60  eggs  remaining.     How  many  had  each  at  first  ? 

16.  |  of  a  number -f  14  =  44;  what  is  that  number? 

17.  A  boy,  being  asked  his  age,  replied,  that  3 
dmes  his  age  —  7  years  was  23  years.     How  old 
was  he  ? 

18.  A,  being  asked  how  much  money  he  had,  re 
plied,  that  twice  what  he  had  -\-  $60,  was  four  times 
$400 ;  how  much  had  he  ? 

19.  Two  boys  have  49  marbles,  but  the  first  has  7 
the  most ;  how  many  has  each  ? 

20.  A  man  bought  a  sheep,  a  cow,  and  a  horse  for 
$70 ;   the  cow  cost  $10  more  than  the  sheep,  and  the 
horse  cost  $20   more  than  the  cow.     What  was  the 
cost  of  each  ? 

21.  A  man  bought  a  melon  for  18|  cents,  which 
was  only  f  of  as  much  as  his  dinner  cost;  what  was 
the  cost  of  his  dinner  ? 

22.  A  gentleman  bought  a  watch  and  chain   for 
$80  ;   the  chain  cost  ^  as  much  as  the  watch ;   what 
was  the  cost  of  each  ? 

23.  A   farmer  bought  a  plow,   a  harness,  and    a 
horse  for  $58 ;  for  the  harness  he  gave  $6  more  than 
for  the  plow,  and  for  the  horse  $34  more  than  for 
the  harness.     What  did  he  give  for  each  ? 

24.  A  boy  bought  twice  as  many  oranges  as  lemons, 
and  on  his  way  home  ate  4  oranges  and  gave  6  away ; 
and  was  surprised  to  find  that  he  had  only  14  oranges 
remaining.     How  many  of  each  kind  did  he  buy  ? 

25.  5  times  a  certain  number  —  12  is  48 ;  wliat  is 
that  number  ? 

26.  J  of  a  certain  number  — 5  is  40  ;  what  is  that 
number  ? 


114  ARITHMETIC. 

27.  A  boy,  .being  asked  his  age,  replied,  that  11 
years  were  7  years  more  than  f  of  his  age  ;  how  old 
was  he  ? 

28.  A  boy,  being  asked  how  many  sheep  his  father 
had,  replied,  that  40  were  5  less  than  J  of  his  number, 
(low  many  had  he  ? 

29.  A  boy  bought   18  lemons ; — for  |  of  them  he 
paid  3  cents  for  2,  and  for  the   remainder  he  paid  2 
cents   apiece ;  for  what  must  he  sell  them  apiece  to 
gain  10  cents  on  the  whole? 

30.  James,  John,    and   Joseph   together   have    96 
peaches ;   James  has  2   more  than  John,  and  Joseph 
has  as  many  as  James  and  John  both  :  how  many  has 
each] 


LESSON    V. 

1.  If  a  man  can  do  a  certain  piece  of  work  in  12 
days,  what  part  of  it  can  he  do  in  1  day  ? 

2.  If  a  man  can  drink  a  barrel  of  beer  in  20  weeks, 
what  part  of  it  can  he  drink  in  1  week  ? 

3.  If  it  require  9  hours  to  empty  a  vessel,  what  part 
of  it  can  be  emptied  in  1  hour  ? 

4.  If  a  family  consume  a  barrel  of  pork  in  30  days, 
what  part  of  a  barrel  do  they  dajly  consume  ? 

5.  If  it  require  19  days  to  perform  a  certain  jour 
ney,  what  part  of  it  can  be  performed  in  1  day  ? 

6.  If  A  can  do  a  certain  piece  of  work   in  8  days, 
and  B  could  do  the  same  in  12  days ;  what  part  of  it 
could  each  do  in  a  day  ? 

7.  If  C  could  mow  a  certain  field  in  4  days,  and  D 
could  do  the  same  in  6  days;   what  part  of  it  could 
each  do  in  .a  day,  and  how  much  could  they  together 
do  in  a  day  ? 

8.  If  C  and  D  can,  in  1  day,  mow  T5^  of  a  field,  how 
(ong  would  it  take  them  to  mow  the  whole  field  ? 


ARITHMETIC.  115 

9.  How  many  days  would  it  take  to  perform  a  cer 
tain  piece  of  work,  if  T\  of  it  can  be  performed  in  1 
day? 

10.  If  George  can  do  a  certain  piece  of  work  in  3 
days,  and  Granvil  can  do  the  same  in  6  days  ;  what 
part  of  it  can  they  together  do  in  1  day,  and  how  long 
would  it  take  them  to  do  the  whole  work  ? 

11.  If  James  can  eat  a  bushel  of  apples  in  10  days, 
and  Ruben  in  12  days ;  how  long  would  1  bushel  last 
them  both  ? 

12.  A  can  cut  a  field  of  wheat  in   12  days,  and  B 
can  do  the  same  in  20  days ;  how  long  would  it  take 

hem  to  cut  the  field  when  they  work  together  ? 

13.  A  merchant  bought  a  hogshead  of  molasses  for 
&20,  10  gallons  of  which  leaked  out ;  how  must  he 
;ell    the  remainder  a  gallon   to  gain   $6,50  on   the 

whole  ? 

14.  £  of  a  barrel  of  flour  cost  $4f,  what  will  f  of  a 
•arrel  cost  ? 

15.  A  and  B  can  build  a  boat  in  20  days,  but  with 
he  assistance  of  C,  they  can  do  it  in  8  days.     How 
ong  would  it  take  C  to  do  it  alone  ? 

10.  A  farmer  and  his  son  can  do  a  piece  of  work 
n  6  days ;  the  son,  alone,  can  do  the  same  in  27 
days.  How  long  would  it  take  the  father  alone  to  do 
the  same  ? 

17.  Three  pipes,  A,  B,  and  C  can  fill  a  cistern  in  2 
lours,  A  and  B  can  fill  the  same  in  4  hours,  and  A 
and  C  can  fill  the  same  in  3  hours.     How  long  would 
t  take  each  to  fill  it  ? 

18.  If  a  barrel  of  beer  would  last  a  man  35  days, 
and,  the  man  and  his  son  20  days  ;  how  long  would  it 
ast  the  son  alone  ] 

19.  A  box  of  tea,  usually,  lasted  a  man  and  his 
tvife  9  months ;  when  the  man  was  absent  it  would 
ast  the  wife  12  months.     How  long  would  it  have 
asted  the  man  alone  ? 


116  ARITHMETIC* 

20.  A,  B,  and  C  can  build  a  boat  in  20  days,  A  and 
B,  in  40  days,  and  A  and  C,  in  30  days.     How  long 
would  it  take  each  separately  to  build  it  ? 

21.  Providing  A  could  drink  a  barrel  of  beer  in  24 
days,  and  B,  in  36  days;  how  long  would  it  take 
them  together  to  empty  a  barrel,  after  i  of  it  had 
leaked  out  ? 

22.  A  market-woman  bought  30  oranges,  and  had 
J  of  them  stolen  ;  the  remainder  she  sold  at  8  cents 
each  and  thereby  gained  |  of  a  cent  on  each  orange 
bought.     What  did  they  cost  apiece  ? 

23.  A  can  do  a  certain  piece  of  work  in  8  days, 
and  A  and  B  together  can  do  the  same,  in  5  days. 
After  A  did  ±  of  the  work,  B  did  the  remainder ;  how 
long  did  it  take  him  ? 

24.  If  A  can  do  a  certain  piece  of  work  in  £  of  a 
day,  how  much  can  he  do  in  1  day  ? 

25.  If  a  man  can  chop  a  cord  of  wood  in  |  of  a 
day,  how  much  can  he  chop  in  1  day  ? 

26.  Isaac  can  make  a  pair  of  boots  in  f  of  a  day, 
and  Ira,  in  |  of  a  day ;  how  many  pair  can  they  both 
make  in  1  day  ? 

27.  Samuel  can  cut  a  cord  of  wood  in  f  of  a  day, 
and  Theodore,  in  |  of  a  day  ;  how  long  would  it  take 
them  to  cut  a  cord,  when  they  work  together  ? 

28.  If  |  of  an  apple  cost  |  of  a  cent,  what  will  | 
of  an  apple  cost  1 

29.  A  can  mow  1  acre  of  grass  in  |  of  a  day,  B,  in 
|  of  a  day,  and  C,  in  f  of  a  day.     How  much  more 
can  A  and  B  mow  in  a  day  than  C  ? 

30.  If  a  wolf  can  eat  a  sheep  in  J  of  an  hour,  and 
a  bear  can  eat  it  in  J  of  an  hour,  how  long  would  it 
take  them  together  to  eat  what  remained  of  a  sheep, 
after  the  wolf  had  been  eating  £  of  an  hour  ? 


ARITHMETIC.  117 


LESSON    VI. 


1.  Lewis,  meeting  some  beggars,   gave  each  of 
(hem  2  cents,  and  had  12  cents  remaining  ;  if  he  had 
given  them  4  cents  each,  it  would  have  taken  all  the 
money  he  had.     How  many  beggars  were  there  ? 

SOLUTION.  —  By  the  last  condition  of  the  question,  he  gavo  each  be/jgar 
2  cents  more  than  by  the  first,  and  to  them  all,  12  cents  more  than  by  the 
first  condition.  Therefore  there  must  have  been  as  many  beggars  as  2  is 
contained  in  12,  which  are  6  beggars. 

2.  A  boy  gave  to  each  of  his  playmates  3  cents, 
and  had  24  cents  remaining ;  if  he  had  given  them 
each  7  cents,  it  would  have  taken  all  the  money  he 
had.     How  many  playmates  had  he  ? 

3.  Mary  gave  each  of  her  playmates  5  apples  ;  ii 
she  had   given  them  each  7  apples,  it  would  have 
taken  12  apples   more.     How  many  playmates  had 
'she  ? 

4.  A  certain  number  of  persons  gave  me  10  cents 
each;  had   they   given  me, 12  cents  each,  it  would 
have  amounted  to  20  cents  more.    How  many  persons 
were  there  ? 

5.  f  of  100  is  -jf  7  of  j  times  the  yearly  salary  of 
the  President  of  the  United  States.    What  is  his  salary  ? 

6.  $40  is  J  times  TJ7  of  the  salary  yearly  received 
by  the  Vice  President  of  the  United  States.     What  is 
his  salary  ? 

7.  Divide  35  oranges  between  James  and  Joseph,  so 
that  James  may  have  15  more  than  Joseph. 

8.  A  cask  of  wine  was  sold  for  $96,  which  was  J  as 
much  again  as  it  cost ;  what  did  it  cost  ? 

9.  A  quantity  of  cotton  was  sold   for  $560,   and 
thereby  gained  J  of  what  it  cost ;  what  did  it  cost  ? 

10.  A  and  B  are  197  miles  apart,  and  are  traveling 
towards  each  other  ;  one  at  the  rate  of  8  miles  an  hour, 
and  the  other,  9  miles  an  hour ;  how  many  hours  be- 
fore  they  will  meet  ? 


118  ARITHMETIC. 

11.  Agnes  gave  2  dimes  a  yard  for  a  piece  of  call- 
co ;  had  she  given  3  dimes  a  yard,  it  would  have  cost 
her  20  dimes  more  ,  how  many  yards  did  the  piece 
contain  ? 

12  A  was  ordered  to  buy  a  certain  number  of 
ranges ;  if  he  bought  those  at  2  cents  each,  he  would 
nave  had  no  money  left, — had  he  bought  those  at  3  cents 
each,  he  would  have  wanted  10  cents  more  to  have 
paid  for  them.  How  many  oranges  was  he  required 
to  buy  ? 

13.  A  lady  wished  to  buy  a  certain  number  of  yards 
of  muslin  ;  there  were  two  kinds,  some  at  9  cents  a 
yard,  and  some  at  12  cents  a  yard.     Had  she  taken 
that  at  12  cents  a  yard,  it  would  have  cost  36  cents 
more  than  the  other  kind.     How  many  yards  did  she 
wish  to  buy  ? 

14.  A  boy,  being  sent  to  market  to  buy  a  certain  num 
ber  of  pounds  of  meat,  found,  if  he  bought  beef  at  5 
cents  a  pound,  he  would  have  39  cents  remaining,  but  it 
he  bought  pork,  at  8  cents  a  pound,  he  would  have  only 

6  cents  remaining.    For  how  much  meat  was  he  sent  t 

15.  If  8  times  a  certain  number,  is  36  more  than  5 
times  the  same  number  ;  what  is  that  number  ? 

16.  A  boy,  being  asked  his  age,  said,  that  4  times 
his  age  was  24  years  more  than  2  times  his  age ;  how 
old  was  he  ? 

17.  A  boy,  being  asked  how  many  sheets  of  paper 
he  had,  said,  that  4  times  the  number,  was  18  less  than 

7  times  the  number  ;  how  many  sheets  of  paper  had 
he? 

18.  A  person,  wishing  to  buy  some  butter,  found,  if 
he  bought  that  which  was  10  cents  a  pound,  he  would 
have  20  cents  remaining  ;  but  if  he  bought  that  which 
was  12  cents  a  pound,  he  would  lack  14  cents  of  hav 
ing  money  enough  to  pay  for  it.     How  many  pound* 
did  he  wish  to  buy  ? 

19.  A  farmer,  wishing  to  buy  a  certain  number  of 


ARITHMETIC. 


sheep,  found  if  he  gave  $2  a  head,  he  would  have  $20 
remaining  ;  but  if  he  gave  $5  a  head  he  would  lack 
$40  of  having  money  enough  to  pay  for  them.  How 
many  sheep  did  he  wish  to  buy  ? 

20.  A,  B,  and  C,  talking  of  their  ages  ;  says  A  to  B, 
am  4  times  as  old  as  you  ;  says  B  to  C,  I  am  J  as 
old  as  you,  but  says  A  to  C,  I  am  40  years  older  than 
you.     Required  the  age  of  each. 


LESSON    VII. 

1.  A  laborer  agreed  to  work  for  40  days  upon  this 
condition  ;  that  for  every  day  he  worked,  he  should 
receive  $2,  and  for  every  day  lie  was  idle,  he  should 
pay  $1  for  his  board.     At  the  expiration  of  the  time, 
he  received  $50.     How  many  days  did  he  work  ? 

SOLUTION. — If  he  had  labored  the  whole  time,  he  would  have  received 
40  times  $2  which  are  $80.  But  he  received  only  $50  :  he,  therefore, 
lo&t  by  his  idleness  $80— $50,  which  is  $30.  For  every  day  he  was  idle 
he  lost  $2  (his  daily  wages)  4-$!  (the  cost  of  his  board)  which  are  $3.  If 
in  1  day  he  lose  $3  ;  he  will  lose  $1  in  $  of  a  day,  and  $30  in  30  times  %  of 
a  day,  which  are  10  days.  Therefore  he  was  idle  10  days,  and  worked 
40 — 10  days,  which  is  30  days. 

2.  A  man  agreed  to  work  60  days,  on  this  condi 
tion  ;  that  for  every  day  he  worked,  he  should  re 
ceive  $1|,  and  for  every  day  he  was  idle,  he  should 
pay  $•*•  for  his  board.     At  the  expiration  of  the  time, 
he  received  $68.     How  many  days  did  he  work  ? 

3.  A  man  was  hired  for  80  days,   on  this  condi 
tion  ;  that  for  every  day  he  worked,  he  should  receive 
6  dimes,  and  for  every  day  he  was  idle,  he  should 
forfeit  4  dimes.     At  the  expiration  of  the  time,  he  re 
ceived  $40.     How  many  days  did  he  work  ? 

4.  How  many  times  f  of  12  is  £  of  48  ? 

5.  A   and   B  bought  a  quantity  of  flour  for  $50 ; 
A  paid  $1  as  often  as  B  f  of  a  dollar ;  what  part  of 
the  flour  belong?  to  each  ? 


120  ARITHMETIC. 

6.  A,  B,  and  C  built  a  house,  which  cost  $500,  of 
which  B  paid  $100  more  than  A,  and  C  paid  as  much 
as  A  and  B  both ;  how  much  did  each  pay  ? 

7.  A  merckam  sold  a  quantity  of  cloth  for  $84, 
and  thereby  lost  f  of  what  it  cost ;  what  did  it  cost  ? 

8.  7£  is  2£  times  f  of  what  number  ? 

9.  A  farmer  having  in  his  employ  an  equal  num. 
ber  of  men  and  boys ;  to  each  boy  he  gave  $4,  to  each 
man  $8  ;  and  to  them  all  he  gave  $84  :  how  many 
men  were  there  ? 

10.  Two  men  hired  a  pasture  for  $35 ;  one  put  in 
3  cows,  and  the  other  put  in  4;  how  much  ought 
each  to  pay  ? 

11.  A  man  sold  an  equal  number  of  ducks  and 
turkeys   for  20  dimes ;   the  ducks,  at  2  dimes  each, 
and  the  turkeys,  at  3  dimes  each :  how  many  did  he 
still  in  all  ? 

12.  A  farmer  sold  an  equal  number  of  ducks  and 
turkeys ;  the  ducks,  at  4  dimes  each,  the  turkeys,  at 
7  dimes  each  ;   and   for  the  turkeys  he  received  $3 
more  than  for  the  ducks :  how  many  of  each  kind  did 
he  sell  ? 

13.  There    are   two   baskets,    which   contain    37 
apples  ;    one  of  which  contains   17  the  most :   how 
many  apples  are  there  in  each  ? 

14.  Charles  and  Henry  together  have  49  marbles, 
and   Charles   has  7  more   than   twice  as   many   as 
Henry  :   how  many  has  each  ? 

15.  Philip  has  20  apples  more  than  Philo ;   and 
they  together  have  92  :  how  many  has  each  ] 

10.  Three  boys  have  47  lemons  ;  the  first  has  3 
more  than  the  second,  and  the  second  has  7  more 
than  the  third  :  how  many  has  each  ? 

17.  A  boy  was  hired  for  20  days,  on  this  con- 
dition  ;  that  for  every  day  he  labored,  he  should  re- 
ceive  3  dimes,  and  for  every  day  he  was  idle,  he 
should  pay  2  dimes  for  his  bo/ard.  At  the  expiration 


ARITHMETIC.  121 

of  the  time  he  received  only  $1.     How  many  days 
was  he  idle  ? 

18.  A  boy  bought  a  whistle,  a  whip,  and  a  drum 
for  70  cents.     For  the  whip  he  gave  twice  as  much 
as  for  the  drum,  and  for  the  drum,  twice  as  much  as 
for  the  whistle  ;  what  did  he  give  for  each  ? 

19.  The  sum  of  three  numbers  is  54.     The  first  is 
twice,  and  the  third,  3  times  the  second ;  what  are 
those  numbers  ? 

20.  Sarah's  age  is  f  of  Susan's,  and  the  sum  of 
tneir  ages  is  24 ;  what  is  the  age  of  each  ? 

21.  £  of  an  army  was  killed,  f  of  the  remainder 
taken  prisoners,  and  400  escaped.     How  many  were 
there  in  the  whole  army  ? 


LESSON  VIII. 

1.  A  fishing  rod,  the  length  of  which  was  14  feet, 
was  broken  into  two  pieces.     The  shorter  piece  was  J 
of  the  length  of  the  longer.     What  was  the  length  of 
each  piece  ? 

SOLUTION. — The  length  of  the  shorter,  which  is  f  of  the 
longer,  added  to  f  (the  length  of  the  longer)  is  J  of  the 
length  of  the  longer,  which  is  the  length  of  both,  which 
is  14  feet.  If  J  of  the  longer  is  14  feet,  j  is  |  of  14  feet, 
which  is  2  feet,  f  (the  length  of  the  longer)  is  4  times  2 
feet,  which  are  8  feet,  &c. 

2.  A  pole  the  length  of  which  is  20  feet,  is  in  the 
air  and  water  f  of  the  length  in  the  air,  equals  the 
length  in  the  water ;  what  is  the  length  in  the  air  and 
water  respectively  ? 

3.  If  in  2  days  a  man  traveled  160  miles,  and  J  of 
the  distance  he  traveled  the  first  day,  equals  the  dis 
tance  he  traveled  the  second  day;  how  far  did  he  travel 
each  day  ? 


122  ARITHMETIC. 

4.  B  and  C  together  have  40  marbles ;  how  many 
has  each,  providing  J  of  B's  number  is  equal  to  C's 
number  ? 

5.  From  New  York  City  to  Redhook  is  100  miles, 
and  J  of  the  distance  from  New  York  to  Rhinebeck, 
equals  the  distance  from  there  to  Redhook.     How  far 
from  Rhinebeck  to  New  York,  and  how  far  from  Rhine, 
beck  to  Redhook  ? 

6.  If  a  horse  and  a  colt  were  worth  $90,  and  the 
horse  was  worth  li  times  as  much  as  the  colt ;  what 
was  the  value  of  each  ? 

7.  A  boy  paid  70  cents  for  a  slate  and  a  book  ;  how 
much  did  he  pay  for  each,  providing  the  book  cost  1 J 
times  as  much  as  the  slate  ? 

8.  If  a  traveler  pay  $1,20  for  his  breakfast  and 
dinner  ;  what  did  he  pay  for  each,  providing  his  din 
ner  cost  £  as  much  as  his  breakfast  ? 

9.  A  pole,  the  length  of  which  is  57  feet,  is  in  the  ai 
\nd  water ;  f   Of  what  is  in  the  air  +  7  feet  equals 
what  is  in  the  water.     Required  the  length  in  the  air, 
and  in  the  water. 

10.  Divide  the  number  108  into  two  such  parts,  that 
^  of  the  first  +  8  shall  equal  the  second. 

11.  Divide  the  number  97  into  two  such  parts,  thai 
^  of  the  first  +  7  shall  equal  the  second. 

12.  There  is  a  fish  the  length  of  which  is  18  feet , 
its  tail  is  4  feet,  and  f  of  the  length  of  the  body,  equals 
the  length  of  the  head.     What  is  the  length  of  the 
head  and  body  respectively  ? 

1 3.  There  is  a  fish  the  weight  of  which  is  1 1  pounds, 
and  i  of  the  weight  of  the   head  +  8  pounds   equals 
the  weight  of  the  body ;  what  is  the  weight  of  each  ? 

14.  A  ship-mast  51  feet  in  length,  in  a  storm,  was 
broken  off,  and  f  of  what  was  broken  off,  equaled  f  of 
what  remained ;  how  much  was  broken  off,  and  how 
much  remained  ? 

15.  A   boy,   being   asked   how   many  apples   and 


ARITHMETIC.  123 

oranges  he  had,  answered,  that  in  all  he  had  38,  and, 
that  f  of  the  number  of  apples,  equaled  £  of  the  num 
ber  of  oranges ;  how  many  of  each  kind  had  he  1 

16.  |  of  one  number  equals  f  of  another,  and  their 
sum  is  57 ;  what  are  the  two  numbers  ? 

17.  A  farmer  has  290  sheep  in  two  different  fields  ; 
and  J  of  the  number  in  the  first  field,  equals  «j  of  the 
number  in  the  second  ;  how  many  are   there  in  each 
field? 

18.  A  market   woman  was  requested   to  buy  ?3 
fowls,  consisting  of  two  different  kinds  ;  J  of  the  num 
ber  of  the  first  kind,  was  to  equal  |  of  the  second 
kind  y  how  many  of  each  kind  must  she  buy  ? 

19.  A  person,  being  asked  the  time  of  day,  said, 
the  time  past  noon  is  ^  of  the  time  past  midnighi ; 
what  was  the  hour  ? 

REMARK. — Since  the  time  past  noon  is  |  of  the  time 
past  midnight,  the  time  from  midnight  to  noon,  which 
is  12  hours,  must  be  %  of  the  time  past  midnight. 

20.  A  person,  being  asked  the  hour  of  the  day,  said, 
the  time  past  noon,  is  £  of  the  time  past  midnight ; 
what  was  the  hour  ? 

21*  A  person,  being  asked  the  hour  of  the  day,  said, 
the  time  past  noon,  is  1  of  the  time  from  now  to  mid 
night  ;  what  is  the  hour  ? 

SOLUTION. — From  that  time  to  midnight  is  f,  and  J 
added  (the  time  past  noon)  is  f .  Consequently  from  noon  to 
midnight  (which  is  12  hours)  is  f  of  the  time  it  lacked  of 
being  midnight,  and  l  of  the  time,  is  j  of  12,  which  is  3 
hours,  the  time  past  noon. 

22.  What  is  the  time  of  day,  providing  J  of  the 
time  from  now  to  midnight  equals  the  time  past  noon  ? 

23.  A  man,  being  asked  the  hour  of  the  day,  said, 
that  *  of  the  time  past  noon,  equaled  J  of  the  time 
from  now  to  midnight ;  what  was  the  time  ? 

24.  A  pole  the  length  of  which  was  68  feet  was  in  the 
air  and  water ;  |  of  the  length  in  the  air,  equaled  J  of 


£24  ARITHMETIC. 

the  length  in  the  water.     What  was  the  length  in  the 
air,  and  in  the  wetter  respectively  1 

25.  The  sum  of  two  numbers  is  176,  and  £  of  the 
first  +  4  equals  f  of  the  second ;    what  are  those 
numbers?  ., 

26.  A  person,  being  asked  the  time  of  day,  said, 
that  ^  of  the  time  past  midnight  equals  ,\  of  the  time 
from  now  to  midnight  again  ;  what  was  the  time  ? 

27.  Providing  the  time  past  10  o'clock  equals  f  of 
the  time  to  midnight ;  what  o'clock  is  it  ? 

28.  Say*  A  to  B,  f  of  my  age  +  4  years  equals  f 
of  yours,  and  the  sum  of  our  ages  is  74  years.     What 
is  each  of  their  ages? 

29.  A  person,  being  asked  the  hour  of  the  day,  re- 
plied,  that  *  of  the  time  past  noon,  equaled  {•  of  the 
time  from  then  to  midnight  +  2}  hours ;  what  was 
the  time  ?  .      , 

30  A  pole  the  length  of  which  is  78  feet,  is  in  the 
air  and  water;  f  of  what  is  in  the  air  + -12  feet, 
equals  \\  times  the  length  in  the  water.  TV  hat  is  the 
length  in  the  air,  and  water  respectively  ? 


LESSON    IX. 

1  There  is  a  fish  the  head  of  which  is  4  inches  long, 
and  whose  tail  is  as  long  as  its  head  +  ±  of  its  body, 
and  whose  body  is  as  long  as  its  head  and  tail  I  >tfc  ; 
what  is  the  length  of  the  fish 


SOLUTION  —By  a  condition  of  the  question,  1  of  tfre 
nrth  of  body  +  4  inches,  is  the  length  of  the  tail  5  and  4 
i  more  Idled,  (the  length  ^^^jA 

*  The  head  of  a  fish  is  6  inches  long,  the  tail  is  as 


AEITHMBTIC.  125 

long  as  the  head  +  £  of  the  body,  and  the  boly  is  as 
long  as  the  head  'and  tail  together  ;  what  is  the  length 
of  the  fish  ? 

3.  The  head  of  a  fish  is  12  inches  long,  the  tail  is  as 
long  as  the  head  +  £  of  the  body,  and  the  body  is  as 
long  as  the  head  and  tail  both  ;  what  is  the  length  of 
the  fish  ? 

4.  The  head  of  a  fish  weighs  10  pounds,  the  tail 
weighs  as  much  as  the  head  -f-  f  as  much  as  the  body ; 
and  the  body  weighs  as  much  as  the  head  and  tail 
both  ;  what  is  the  weight  of  the  tail  ? 

5.  |  of  a  certain  number  equals  $  of  the  same  num 
ber  +  10  ;  what  is  that  number  ? 

6.  A  boy,  being  asked  his  age,  replied,  that  *•  of 
his  age,  exceeded  J  of  his  age  by   4   years ;  how  old 
was  he  ? 

7.  James,    being    asked    how   many    arimmetical 
questions  he  had  answered  properly  during  the  week, 
replied,  that  £  of  the  number,  was  3  more  than  f  of 
the  number  ;  how  many  questions  had  he  answered  ? 

8.  A  farmer,  after  selling  |  of  11  times  as  much 
grain  as  he  had,   had  80   bushels  remaining ;    how 
much  had  he  at  first  ? 

9.  An  individual,  after  spending  f  of  all  his  money, 
and  |  of  what  then  remained,  had  only  $12|  remain* 
ing  ;  how  much  had  he  at  first  ? 

10.  If  |  of  a  ship  be  worth  £  of  her  cargo,  valued 
at  300  eagles ;  what  is  the  value  of  the  ship  ? 

11.  Dick,  being  asked   how  much  money  he  had, 
said,  its  £  exceeded  its  f  by  $2 ;  how  much  had  he  ? 

12.  A  tree  by  falling,  was  broken  into  three  pieces ; 
the  top  part  was  10  feet  long,  the  bottom  part  was  as 
long  as  the  top  +  f  of  the  middle,  and  the  middle  part 
was  as  long  as  the  other  two :  what  was  the  length  of 
the  tree,  and  of  each  piece  ? 

13.  A  man  bought  a  hat,  a  coat,  and  a  watch  ;  the  hat 
cost  $6,  the  watch  cost  as  much  as  the  hat  -f-  }  of  the 


126  RITHMETIC. 

cost  of  the  coat,  and  the  coat  cost  as  much  as  the  hat 
and  watch  both  ;  what  was  the  cost  of  each,  and  of  all  ? 

14.  |  of  J  is  how  many  times  }  ? 

15.  If  f  of  a  ton  of  hay  cost  j  of  an  eagle,  how 
many  dollars  will  4  of  a  ton  cost  'I 

16.  A  third  and  £  of  a  third  of  10  is  }  of  what 
number  ? 

17.  If  from  a  certain  number  you  take  its  \  and 
its  £,  the  remainder  will  be  13£,  what  is  that  number  ? 

18.  After  spending  |  of  my  money,  I  earned  |  as 
*nuch  as  I  spent,  and  then  had  only  $20  less  than 
what  I  had  at  first ;  how  much  had  I  at  first  ? 

19.  The  head  of  a  fish  is  8  inches  long,  the  tail  is 
as  long  as  the  head  and  ^  of  the  body  -f-  10   inches, 
and  the  body  is  as  long  as  the  head  and  tail  both ;  what 
is  the  length  of  the  fish  ? 

20.  The  head  of  a  fish  is  12  inches  long ;  its  tail  in 
10  inches  longer  than  its  head  increased  by  J  the  length 
of  the  body;  and  its  body  Li  20  inches  longer  tl*m  fta 

r;ul  nn*l  ta'1  h»"ftlv>r      \V!'**  i<  tin*  1-ncth  •  •('  UK-  fl4i  ? 


LESSON   X. 

1.  James  is  20  years  old,  and  John  is  4  years  old', 
in  how  many  years  will  James,  who  is  now  5  times  as 
old  as  John,  be  only  twice  as  old  ? 

REMARK.— Four  years  ago  James  was  16,  and  in  16  years  more  ho  will 
be  twice  as  old  as  John. 

2.  Sarah  is  10  years  old,  and  Sally  is  4 ;   in  how 
many  years  will  Sally  be  4  as  old  as  Sarah  ? 

8.  Jacob  is  40  years  old,  and  Alfred  is  2  ;  in  how 
many  years  will  Alfred  be  ^  as  old  as  Jacob  ? 

4.  If  the  third  of  6  be  3,  what  will  the  fourth  of 
20  bo? 

6.  If*  of  12  be  10,  what  will  f  of  10  be  ? 

4.   VV  hat  is  a  third  and  a  half  of  1}  times  1C  ? 


ARITHMETIC.  127 

7.  Divide  the  numoer  85  into  two  parts,  that  shall 
be  to  each  other  as  |  to  J. 

8.  When  A  was  married,  he  was  3  times  as  old  aa 
his  wife,  but  when  they  had  been  married  15  years, 
he  was  only  twice  as  old  as  she  was ;   how  old  was 
each  when  they  were  married  ? 

REMARK.— The  conditions  of  the  above  question  jive  the  following: 

9.  Three  times  a  certain  number  -f-  15  equals  twice 
the  same  number  -f-  30 ;  what  is  that  number,  and 
what  is  3  times  the  same  number  ? 

10.  Once  times  a  certain  number  +  15  equals  \  of 
the  same  number  -f  30 ;  what  is  that  number,  and 
what  is  \  of  the  same  number? 

11.  When  I  first  met  Mr.  A,  I  was  |  as  old  as  he 
was,  and  in  12  years  after  that,  I  was  j  as  old  as  he 
was  ;  what  was  each  of  our  ages  when  we  first  met  ? 

12.  There  are  two   numbers,  one  of  which  is  4 
times  the  other ;  but  if  to  each  20  were  added,  one  will 
be  double  the  other :  what  are  these  numbers? 

13.  When  B  was  married,  he  was  3  times  as  old  aa 
his  wife ;  but  after  they  had  been  married  60  years, 
|  of  his  age  equaled  hers ;  what  was  the  age  of  each 
when  they  were  married  ? 

14.  A  hound  takes  3  leaps  to  a  fox  4,  and  3  of  the 
hound's  leaps  are  equal  to  6  of  the  fox's ;   how  many 
leaps  must  the  hound  take  to  gain  I  on  the  fox  ? 

15.  If  the  hound  takes  1£  leaps  to  gain  1,  on  the 
fox  ;  how  many  must  he  take  to  gain  20  on  the  fox  ? 

16.  A  hare  is  20  leaps  before  a  hound,  and  takes  4 
leaps  to  the  hound  3 ;  and  3  of  the  hound's  leaps  are 
equal  to  6  of  the  hare's.     How  many  leaps  must  the 
hound  take  to  catch  the  hare  ? 

17.  A  fox  is  60  leaps  before  a  hound,  and  takes  5 
leaps   to  the  hound  2 ;  and  4  of  the  hound's    leaps 
equals  12  of  the  fox's.     How  many  leaps   must  the 
hound  take  to  catch  the  fox  ? 

18.  Alfred  is  60  steps  before  Silas,  and  takes  9 


128  ABTTHMETIC. 

steps  to  Silas  6  ;  and  3  of  Silas'  steps  equals  7  of 
Alfred's.  How  many  steps,  at  this  rate,  will  each  take 
before  they  will  be  together  ? 

HrMARK. — Ji  box  of  glass  contains  50  square  feet,  or  as  nearly  qs  may  be. 

19.  How  many  panes  of  glass  in  a  box,  providing 
they  are  6,  by  8  inches  ? 

REMARK. — Find  the  area  of  a  pane  of  glass  by  reducing 
the  inches  to  parts  of  a  foot,  and  then  multiply  these  parts 
together.  The  area  of  a  pane  6  by  8  inches  is  £  of  a 
square  foot.  The  remainder  may  be  solved  as  follows : 

SOLUTION. — If  1  pane  is  ^  of  a  square  foot,  to  make  f, 
(a  square  foot,)  it  will  take  3  times  1  pane  which  are  3 
panes;  and  to  make  50  square  feet,  (1  box,)  it  will  require 
50  times  3  panes,  which  are  150  panes. 

20.  How  many  panes  of  glass  in  a  box,  providing 
they  are  8,  by  10  inches  ? 

21.  How  many  panes  of  glass  in  a  box,  providing 
they  are  10,  by  12  inches  ? 

22.  How  many  panes  of  glass  in  a  box,  providing 
they  are  8,  by  12  inches  ? 

23.  How  many  panes  of  glass  in  a  box,  providing 
they  are  12,  by  15  inches  ? 


LESSON    XI. 

1.  What  number  is  that,  to  which  if  its  £  be  added 
the  sum  will  be  15  ?  ^ 

2.  What  number  is  that,  to  which  if  its  \  be  added, 
the  sum  will  be  24  ? 

3.  What  number  is  that,  to  which  if  its  J  be  added> 
the  sum  will  be  40  ? 

4.  What  number  is  that,  to  which  if  its  J  be  added, 
the  sum  will  be  30  ? 

5.  What  number  is  that,  to  which  if  its  j  be  added, 
the  *um  will  be  77  ? 


ARITHMETIC.  129 

6.  How  old  is  that  man,  to  whose  age  if  you  add 
its  ^  and  its  f ,  the  sum  will  be  104  years  ? 

7.  What  number  is  that,  which  being  increased  by 
its  £,  its  i  and  18  more  will  be  doubled  ? 

8.  A  man,  being  asked  his  age,  said,  that  if  his  age 
were  increased  by  its  |  and  20  more,  the  sum  would 
be  double  his  age.     What  was  his  age  ? 

9.  Suppose  I  buy  a  certain  number  of  boxes  of  but 
ter,  at  $2  a  box,  and  as  many  more  at  $4  a  box ;  and 
oell  them  all,  at  $3  a  box ;  do  I  gain  or  lose,  and  how 
much  1 

10.  A  boy,  being  asked  how  many  oranges  he  had, 
replied,  that  if  his  number  were  increased  by  its  £, 
its  f ,  and  38  more,  the  sum  would  equal  3  times  his 
number.     How  many  had  he  ? 

11.  Suppose  I  buy  a  certain  number  of  melons  ; 
some  at  10  cents  each,  and  as  many  more  at  40  cents 
each  ;    and  sell  them  all,  at  30  cents  apiece  :  how 
much  do  I  gain  on  each  melon  ? 

12.  If  by  selling   1   apple  I  lose  -^of  a  cent,  how 
many  apples,  at  this  rate,  must  I  sell  to  lose  6  cents  ? 

13.  A  boy  bought  a  certain  number  of  lemons  for 
2  cents  apiece,  and  as  many  more,  at  4  cents  apiece  ; 
and  sold  them  out,  at  the  rate  of  3  for  5  cents  :  did 
he  gain  or  lose,  and  how  much  ? 

14.  A  woman  bought  a  certain  number  of  apples, 
at  the  rate  of  2  for  a  cent,  as  many  more,  at  the  rate 
of  3  for  a  cent ;  and  sold  them  all,  at  the  rate  of  5  for 
2  cents,  and  by  so  doing,  lost  4  cents.     How  many  of 
each  kind  did  she  buy  ? 

15.  A  woman  bought  a  certain  number  of  eggs,  a. 
the  rate  of  3  for  a  cent,  and  as  many  more,  at  4  for  a 
cent ;  and  sold  them  out,  at  the  rate  of  8  for  3  cents, 
and  by  so  doing,  gained  4  cents.     How  many  eggs  did 
she  buy? 

16.  Three  men  agreed  to  share  $510  in  the  propor 
tion  of  ^,  |  and  | ;  how  much  must  each  receive  ? 


ISO  ARITHMETIC. 

17.  A's  fortune  is  to  B's  as  £  to  £ ;   and  they 
together  have  $100  ;  how  much  has,  each  ? 

18.  The  difference  of  two  numbers  is  15,  which  is 
£  of  twice  as  much  as  the  smaller  number ;   what  are 
these  two  numbers  ? 

19.  A  merchant  bought  a  certain  number  of  yards 
of  cloth,  at  the  rate  of  2  yards  for  $1,  and  as  many 
more,  at  the  rate  of  5  for  $1 ;  and  sold  them  all,  at  the 
rate  of  10  yards  for  $3  ;   and  thereby  lost  $8.     How 
many  yards  did  he  buy  ? 

20.  A  man  bought  a  certain  number  of  melons,  at 
\he  rate  of  4  for  $1,  and  as  many  more,  at  the  rate  of 
10  for  $1 ;   and  sold  them  all,  at  the  rate  of  8  for  $2, 
trid  thereby  gained  $6.     How  many  melons  did  he 
ouy? 


LESSON    XII. 

1.  Mary  has  twice  as  many  apples  as  Sarah,  and 
they  together  have  12 ;  how  many  has  each  ? 

REMARK. — By  the  condition  of  the  question  Mary  has  2  apples  as  often 
as  Sarah  1.  Consequently  Mary  must  have  f,  and  Sarah  ^  of  the  13 
apples. 

2.  Divide  18  into  two  such  parts,  that  one  shall  be 
twice  the  other. 

3.  Divide  21  oranges  between  two  boys,  so  that  one 
may  have  twice  as  many  as  the  other. 

4.  Franklin  and  Francis  together  have  15  quarts 
Df  nuts,  but  Franklin  has  twice  as  many  as  Francis ; 
how  many  has  each  ? 

5.  Robert  has  twice  as  many  cents  as  Harry,  and 
they  together  have  24 ;  how  many  has  each  ? 

6.  Divide  the  number  27  into  two  parts,  that  shall 
be  to  each  other  as  1  to  2. 

7.  Harriet  is  twice  as  old  as  Ellen,  and  the  sum  of 
their  ages  is  30  years ;  what  is  the  age  of  each  ? 

8    A  and  B  are  36  rods  apart,  and  travel  towards 


ARITHMETIC.  131 

each  other ;  hew  far  will  each  travel  before  they  meet, 
providing  A  travels  twice  as  fast  as  B  ? 

9.  Whai  number  must  be  added  to  twice  itself,  that 
the  sum  may  be  57  ? 

10.  A,  after  spending  J  of  all  his  money,  and  |  of 
the  remainder  lacking  $4,  had  only  $14  remaining  • 
how  much  had  he  at  first  1 

11.  Divide  the  number  48  in  two  such  parts,  that 
one  shall  be  f  of  the  other. 

12.  In  a  certain  school,  there  are  3  times  as  many 
boys  as  girls,  and  in  all  there  are  52  pupils  ;  how 
many  boys,  and  how  many  girls  in  the  school  ? 

13.  James  and  Jackson   together  have  45  marbles, 
but  James  has  only  £  as  many  as  Jackson  ;  how  many 
has  each  ? 

14.  A  man  and  his  son  together  earned  $280  in  a 
year ;    how  much   does  each  earn,  providing  the  boy 
earns  only  1  as  much  as  his  father  ? 

15.  A  boy  bought   a   melon   and   a  citron  for  $1 ; 
V>w  much  did  each  cost,  providing  the  melon  cost  only 
£  as  much  as  the  citron  ? 

16.  A  man  bought  a  horse  and  a  saddle  for  $120  ; 
the  saddle  cost  only  £  as  much  as  the  horse ;   what 
was  the  cost  of  each  ? 

17.  A  man,  being  asked  the  cost  of  his  oxen,  said,  that 
his  oxen  and  wagon  together  cost  $240,  and  that  the 
oxen  cost  twice  as  much  as  the  wagon  ;  what  was  the 
cost  of  each  ? 

18.  A   man   bought  a  sheep,  a  hog,  and  cow  for 
$42 ;  for  the  hog,  he  gave  twice  as  much  as  for  the 
sheep,  and  for  the  cow,  3  times  as  much  as  for  the 
sheep.     How  much  did  he  give  for  each  ? 

19.  A  farmer  and  his  two  sons  earned  $560  in  1 
year ;  the  father  earned  twice  as  much  as   his  elder 
son,  and  the  elder   son  earned  twice  as  much  as  the 
younger  son.     How  much  did  each  earn  ? 

20.  A,  B,  and  C  together,  in  1  day,  can  dig  10$ 


132  ARITHMETIC. 

bushels  of  potatoes  •  A  digs  \  as  much  as  B,  and  B,  \ 
as  much  as  C.  How  many  bushels  can  each  dig  in 
a  day  ? 

21.  A  man  bought  three  pieces  of  cloth  for  $160; 
the  first  piece  cost  only  1  as  much  as  the  second,  and 
the  second,  only  1  as  much  as  the  third.     What  did 
each  piece  cost  ? 

22.  In  an  army  consisting  of  20,000  men  ;  3  timea 
as  many  were  wounded  as  were  killed,  and  4  times 
as  many  remained  unhurt  as  were  wounded.     How 
many   were    killed,    wounded,   and    unhurt    respect- 
ively  ? 

23.  i  of  A's,  +  |   of  B's  money  equals  $5500  ; 
and  |  of  B's  money  is  4  times  \  of  A's.     What  is 
each  of  their  fortunes  ? 

24.  Herman  and  Byron  together  have  60  blocks ; 
and  Byron  owns  |  as  many  as  Herman ;  how  many 
has  each  ? 

25.  Divide  the  number  60  into  two  parts,  that  shall 
be  to  each  other  as  ^  to  f . 

26.  Adelia  and  Louisa  are  to  share  14  apples  in 
the  proportion  of  4  to  3  ;  how  many  ought  each  to  re- 
ceive  ? 

27.  The  sum  of  Mary's  and  Hezekiah's  age  is  24 
years ;   how  old  is  each,  providing  Hezekiah  is  only 
|  as  old  as  Mary  ? 

28.  Henry  and  his  father  can  thrash  35  bushels  of 
oats  in  a  day ;  how  many  does  each  thrash,  if  Henry 
thrashes  only  |  as  much  as  his  father  ? 

29.  A   pole,  whose  length   is  70  feet,  is  in  the  ail 
and  water;   how  much  is  in  the  air  and  water  re- 
spectively,  if  f  of  what  is  in  the  air  equals  what  is  in 
the  water  ? 

30.  Divide  the  number  36  into  two  parts,  that  shall 
be  to  each  other  as  5  to  4. 

31.  Divide  the  number  45  into  two  parts,  that  shall 
be  to  each  other  as  1  to  f . 


ARITHMETIC.  .  33 

32.  A  and  B  together  own  $450 ;  but  A  owns  only 
J  as  much  as  B :  how  much  belongs  to  each  ? 

33.  A  man  died,  and  left  $7200  to  be  divided  be- 
tween  his  son  and  daughter,  in  the  proportion  of  1  to 
$ .     What  ought  each  to  receive  ? 

34.  In  a  mixture  of  tea  consisting  of  48  pounds, 
there  was  A  as  much  poor,  as  good  tea :  how  much  ol 
each  kind  was  there  ? 

35.  A  man  bought  a  co^r  and  a  horse  for  $96 ;  the 
cow  cost  |  as  much  as  the  horse :  what  was  the  cost 
of  each  ? 

36.  Moses  has  only  ^  as  many  chestnuts  as  Aaron ; 
and  they  together  have  40  quarts :  how  many  belongs 
to  each  ? 

37.  Divide   the  number  49,  into  two  parts,  that 
shall  be  to  each  other  as  1  to  J. 

38.  A  hound  ran  60  rods  before  he  caught  a  fox ; 
and  |  the  distance  the  fox  ran  before  he  was  caught, 
equaled  the  distance  he  was  ahead  when  they  started. 
How  far  did  the  fox  run,  and  how  far  in  advance  of 
the  hound  was  he,  when  the  chase  commenced  ? 

39.  The  sum  of  two  numbers  is  140,  and  the  larger 
is  to  the  smaller  as  1  to  f ;   what  are  the  two  num. 
bers? 

40.  A  and  B  together  owe  $69,  but  B  owes  only  }J 
as  much  as  A  ;  how  much  does  each  owe  ? 

41.  Thomas  and  Thornton  found  $240,  but  could 
not  agree  about  the  division  of  it ;  they  therefore  threw 

.  it  on.  the  floor  and  each  got  what  he  could  ;  it  so  hap 
pened  that  Thomas  got  only  |  as  much  as  Thornton. 
How  much  did  each  get  ? 

42.  In  a  certain  school  consisting  of  48  pupils,  there 
are  1%  times  as  many  boys  as  girls  ;  how  many  boys, 
and  how  many  girls  in  the  school? 

43.  A  gold  and  a  silver  watch  were  bought  for  $160  j 
the  silver  watch  cost  only  ^  as  much  as  the  gold  one ; 
what  was  the  cost  of  each  ? 


J34  ARITHMETIC. 

44.  Divide  the  number  17  into  two  parts,  that  shall 
be  to  each  other  as  |  to  J. 

45.  A  farmer  had  180  sheep  in  two  fields,  and  J  ot 
the  number  in  the  first  field  equaled  }  of  the  nuihb^r 
in  the  second  ;  how  many  in  each  field  ? 

46.  Divide  88   into  two  parts  that  shall  be  to  each" 
other  as  |  to  4. 

47.  |  of  the  distance  a  hare  ran  after  a  hound  start- 
ed  after  her,  equaled  the  Jistance  she  was  before  the 
hound  when  they  started  ;  how  far  did  the  hare  run 
before  she  was  caught,  providing  the  hound  ran  80 
rods  to  overtake  her  ? 

48.  A  and  B  started  from  the  same   point,  and  ran 
in  the  same  direction  ;  B  ran  60  rods  ;  then  T\  of  the 
distance  A  had  run  equaled  the  distance  A  was  ahead 
of  him.     How  much  did  A  gain  on  B  in  running  6tf 
rods? 

41J.  A  fishing  rod,  the  length  of  which  is  24  feet,  i$ 
in  two  parts;  j  of  the  longer  part  equals  the  length  of 
the  shorter.  Mow  long  is  each  part? 

50.  A  hound  ran  90  rods  before  he  caught  a  deer  ,• 
the  deer  ran  44  times  as  far  as  he  was  ahead  of  th^ 
hound  when   they  started,   before  it   was   overtaken. 
How  far  ahead  of  the  hound  was  the  deer  when  the 
chase  commenced  ? 

51.  |  of  A's  number  of  sheep  -f  f  of  B's  number, 
equals  900  ;  how  many  sheep  has  each,  providing  f* 
of  B's  number  is  twice  f  of  A's  number  1 


LESSON    XIII, 


1 .  A  person  had  two  silver  cups,  and  only  one  cov 
er  for  both.  The  first  cup  weighed  6  oz.  If  the  first 
eup  be  covered,  it  will  weigh  twice  as  much  as  the 
second,  but  if  the  second  cup  be  covered  it  will  weigh 


ARITHMETIC. 


135 


3  times  as  much  as  the  first.     What  is  the  weight  of 
the  second  cup,  and  cover  ? 

SOLUTION. — By  the  last  condition  of  the  question,  3  times  the  weight  of 
the  first  cup,  (19  ounces,)  equals  the  weight  of  the  second  cup  and  cover. 
Consequently  the  two  cups  and  cover  weigh  19,  +  6  ounces,  which  are 
24  ounces.  And  by  the  first  condition,  the  first  cup  and  cover  weigh 
twice  as  much  as  the  second  cup.  Therefore  the  24  ounces  must  be  di 
vided  into  two  parts,  which  are  to  each  other  as  2  to  1.  One  of  these 
parts  will  be  the  weight  of  the  second  cup,  and  2,  the  weight  of  the  first 
cup  and  cover,  Sec. 

2.  A  lady  has  two  silver  cups,  and  only  one  cover 
for  both.     The  first  cup  weighs  8  ounces.     The  first 
cup  and  cove^r  weigh  3  times   as  much  as  the  second 
cup ;  and  the  second  cup  and  cover  weigh  4  times  as 
much  as  the  first  cup.     What  is  the  weight  of  the 
second  cup,  and  cover  ? 

3.  A  man  bought  a  hat,  a  coat,  and  a  vest  for  $40. 
The  hat  cost  $6  ;  the  hat  and  coat  cost  9  times  as 
much  as  the  vest.     What  was  the  cost  of  each  ? 

4.  A  boy  bought  a  squirrel,  a  rabbit,  and  a  bird. 
The  squirrel  cost  15  cents.     The  squirrel  and  rabbit 
cost  twice  as  much  as  the  bird  ;  and  the  rabbit  and 
bird  cost  3  times  as  much  as  the  squirrel.     What  was 
the  cost  of  the  bird  and  rabbit  respectively  ? 

5.  A  farmer  bought  a  cow,  an  ox,  and  a  horse  ; 
the  cow  cost  $20.     The  cow  and  ox  together  cost  3 
times   as    much    as   the    horse ;    the   ox    and    horse 
together  cost  4  times  as  much  as  the  cow.     What  was 
the  cost  of  the  ox  and  horse  respectively  ? 

6.  A  man  bought  two  horses  and  a  saddle.     The 
younger  horse  cost  $40.     The  saddle  cost  |  as  much 
as  both  horses  ;  and  the  younger  horse  cost  £  as  much 
as  the  other  horse  and  saddle  together.     What  did  the 
saddle  and  older  horse  cost  respectively  ? 

7.  A   man  traveled  three  successive  days.     The 
first  day  he  traveled  30  miles,  which  was  £  of  the  dis 
tance  he  traveled  the  other  two  days-;  and  4  times  the 
distance  he  traveled  the  second  day  equaled  the  dig- 


136  ARITHMETIC. 

tance  he  traveled  the  first  and  third  days.     How  fa* 
did  he  travel  each  day  ? 

8.  A  is  worth  $1000,  and  B  and  C  together  are 
worth  9  times  as  much  as  A  ;  and  C  is  worth  £  at 
much  as  A  and  B.     How  much  is  B  and  C  worth 

espectively  ? 

9.  A's  coat  cost  $20,  and  his  vest  and  hat  together 
cost  5  times  as  much  as  his  coat ;  and  3  times  thf 
cost  of  his  vest  equaled  the  cost  of  both  coat  and  hat 
What  was  the  cost  of  his  vest  and  hat  respectively ' 

10.  B's  harness  cost  $120,  which  was  £  of  the  cosf 
of  his  horse  and  sleigh  ;  and  the  harness  and  horse 
together   cost   twice   as   much  as   the   sleigh.     How 
much  did  the  horse  and  sleigh  cost  respectively  ? 

11.  A    tree  in    falling    broke    into   three  unequal 
pieces.     The  top  piece  was  8  feet  long,  which  was  J 
of  the  length  of  the  other  two  pieces  ;  and  3  times  the 
length  of  the  bottom  piece,  equals  the  length  of  the 
other  two  pieces.     How  long  was  the  tree,  and  how 
long  was  each  piece  ? 

12.  Find  the  ages  of  A,  B,  and  C,  by  knowing  that 
A  is  20  years  old,  and  that  the  sum  of  B's  and  C's 
age    is  4  times  A's  age  ;  and  that  C's  age  is  £  of  the 
sum  of  A's  and  B's  age. 

13.  Find  the  fortunes  of  A,  B,  C,  D,  E  and  F,  by 
knowing  that,  A  is  worth  $20,  which  is  J  as  much  as 
B  and  C  are  worth,  and  that  C  is  worth  £  as  much  as 
A  and  B  ;  and,  also  that  if  19  times  the  sum  of  A's, 
B7s  and  C's  fortune   were  divided  in  the  proportion  of 
J,  i,  and  ^  it  would  respectively  give  J  of  D's,  £  ol 
E's  and  £  Of  F's  fortune. 


ARITHMETIC.  137 

•% 

CHAPTER    VIII. 
LESSON    I. 

REMARK.— In  our  calculations  on  interest  (as  heretofore  mentioned)  we 
totall  reckon  30  days  to  the  month,  and  1*2  months  to  the  year.  Although^ 
this,  math ematic ally  speaking,  will  not  produce  a  result  strictly  accurate i 
jet  it  will  be  sufficiently  correct,  for  all  practical  purposes. 

1.  Reduce  2  years  and  4  months  to  the  fraction  of 
a  year. 

SOLUTION. — 4  months  is  what  part  of  a  year?  There 
are  12  months  in  1  year,  therefore  1  month  is  A  of  a 
year ;  and  4  months  is  4  times  ^,  which  is  ^  or  |  of  a 
year.  In  2|  years,  how  many  tnlrds  1  In  1  there  are  §, 
therefore  3  times  the  number  of  whole  ones  equal  the  num 
ber  of  thirds.  3  times  2  are  6,  and  J  added  are  J 
years. 

(ft^-  REMARK. — Jlltoays  reduce  a  fraction  to  its  lowest  terms  before 
performing  any  other  operation  with  it.  -£$ 

Pupils  may  not  be  able,  readily  to  discover  the  greatest  number  that 
will  divide  both  numerator  and  denominator,  without  a  remainder.  Con 
sequently,  the  most  expeditious  way  will  be,  to  continue  to  divide  by  the 
least  number  that  is  contained  in  both  numerator  and  denominator 
without  a  remainder,  until  the  fraction  is  reduced  to  its  lowest  terms. 

2.  Reduce  1  year  and  3  months  to  the  fraction  of 
a  year. 

3.  Reduce  3  years  and  5  months  to  the  fraction  of 
a  year. 

4.  Reduce  4  years  and   10  months  to  the  fraction 
of  a  year. 

5.  Reduce  7  years  and  9  months  to  the  fraction  of 
a  year. 

6.  Reduce  8  years  and  8  months  to  the  fraction  of 
a  year. 

7.  Reduce  12  years  and  7  months  to  the  fraction 
of  a  year. 

8.  Reduce  11  years  and  11  months  to  the  fraction 
of  a  year. 

0.  Reduce  6  years  and  6  months  to  the  fraction  of 
a  year. 


138  ARITHMETIC 

10.  Reduce  9  years  and  8  months  to  the  fraction 
of  a  year. 

11.  Reduce  2  years  4  months  and  15  days  to  the 
fraction  of  a  year. 

SOLUTION. — 15  days  is  what  part  of  a  month  *  There 
are  30  days  in  one  month,  therefore  1  day  is  ^  of  a  month, 
and  15  days  is  15  times  ^  which  is  ££,  or  £  of  a  month. 
4 1  months,  or  f  months,  is  what  part  part  of  a  year? 
Tnere  are  12  months  in  one  year,  therefore,  1  month  is  ^ 
of  a  year,  and  |  of  a  month  is  |  of  ^,  which  is  ¥V  of  a 
year ;  and  if  \  of  a  month  is  -^  of  a  year,  9  halves  is  9 
times  gV,  which  is  ^9?,  or  f  of  a  year.  In  2|  years,  how 
many  eighths  ? 

12.  Reduce  4  years  7  months  and  6  days  to  the 
fraction  of  a  year. 

13.  Reduce  5  years  9  months  and  18  days  to  the 
fraction  of  a  year. 

14.  Reduce  1  year  7  months  and  18  days  to  the 
fraction  of  a  year. 

15.  Reduce  2  years  7  months  and  6  days  to  the 
fraction  of  a  year. 

16.  Reduce  3  years  3  months  and  6  days  to  the 
fraction  of  a  year. 

17.  Reduce  5  years  4  months  and  24  days  to  the 
fraction  of  a  year. 

18.  Reduce  6  years  5  months  and  18  days  to  the 
fraction  of  a  year. 

19.  Reduce  7  years  11  months  and  6  days  to  the 
fraction  of  a  year. 

20.  Reduce  10  years  10  months  and  12  days  to 
the  fraction  of  a  year. 


LESSON    II. 

REMARK. — Interest  is  money  due  for  the  use  of  money 
borrowed ;  and  is  estimated,  at  a  certain  rate  per  cent  per 
annum,  which  is  regulated  by  law. 


ARITHMETIC. 


180 


The  snm  on  which  the  interest  is  paid,  is  called  the 
Principal.  The  sum  of  the  principal  and  interest  is  called 
the  Amount. 

By  6.  per  cent  is  meant,  6  cents  on  100  cents,  $6  on  $100, 
or  6  on  100  whatever  he  the  denomination.  Hence,  at  6 
per  cent,  T^  or  -fa  of  the  principal  equals  the  interest. 

When  no  time  is  specified  1  year  is  understood. 

1.  At  4  per  cent,  what  part  of  the  principal  equals 
the  interest  ? 

SOLUTION. — If  the  interest  on  100  cents  is  4  cents,  on  I 
cent  it  is  T|ff  of  4  cents  which  is  TJ7  or  -^  of  a  cent. 
Therefore,  at  4  per  cent,  -^  of  the  principal  equals  the 
interest. 

2.  At  2  per  cent,  what  part  of  the  principal  equals 
the  interest? 

3.  At  5  per  cent,  what  part  of  the  principal  equals 
the  interest  ? 

4.  At  6  per  cent,  what  part  of  the  principal  equals 
the  interest  ? 

5.  At  8  per  cent,  what  part  of  the  principal  equals 
the  interest  ? 

6.  At  10  per  cent,  what  part  of  the  principal  equals 
the  interest  ? 

7.  At  7  per  cent,  what  part  of  the  principal  equals 
the  interest? 

8.  At  12  per  cent,  what  part  of  the  principal  equals 
the  interest  ? 

9.  At  18  per  cent,  what  part  of  the  principal  equals 
the  interest  ? 

10.  At    15  per  cert,  what  part  of  the  principal 
equals  the  interest  ? 

11.  At   25  per  cent,  what  part  of  the  principal 
equals  the  interest  ? 

12.  At   20   per  cent,  what  part  of  the  principal 
equals  the  interest  ? 

13.  At   24  per  cent,  what  part  of  the  principal 
equals  the  interest  ? 


140  ARITHMETIC. 

14.  At   30  per  cent,  what  part  of  the  principal 
equals  the  interest  ? 

15.  At  32  per  cent,  what  part  of  the  principal 
equals  the  interest  ? 

16.  A  man  sold  a  quantity  of  goods,  and  thereby 
gained  75  per  cent  on  the  cost ;  what  part  of  the  cost 
equals  the  gain  ? 

17.  A  man  by  selling  a  horse,  gained  25  per  cent 
on  the  cost ;  what  part  of  the  cost  equaled  the  gain  ? 

18.  A  merchant,  by  selling  a  quantity  of  goods, 
gained  85  per  cent ;  what  part  of  the  cost  equaled  the 
gain? 

19.  By  selling  a  watch,  a  man  lost  15  per  cent  on 
the  cost ;  what  part  of  the  cost  equaled  the  loss  ? 

20.  If  by  selling  a  quantity  of  candies,  a  boy  gains 
120  per  cent  on  the  cost,  what  part  of  the  cost  equals 
the  gain  ? 


LESSON    III. 

.EMARK. — When  we  say  JQ  of  the  principal  equals 
the  interest,  it  will  be  understood,  mat,  a  twentieth  part  of 
the  principal,  whatever  be  the  denomination  will  be  the  in 
terest.  Thus,  if  2^  °f  me  principal  equals  the  interest; — 
the  interest  on  $1  is  -^  of  a  dollar ;  or  on  1  cent,  ^  of  a 
cent,  and  on  100  cents  100  times  ^,  which  is  y^0,  or  5 
cents;  that  is  5  cents  on  100  cents,  or  5  per  cent.  Hfeft 

1.  If /y  of  the  principal  equals  the  interest,  what  is 
the  rate  per  cent  ? 

SOLUTION. — If  on  1  cent  the  interest  is  -£$  of  a  cent,  on 
100  cents  it  is  100  times  /ff  of  a  cent,  which  is  3//j  °r  6 
per  cent. 

2.  If  j\  of  the  principal  equals  the  interest,  what  is 
the  rate  per  cent  ? 

3.  If /j  of  the  principal  equals  the  interest,  what    i 
the  rate  per  cent  ? 


ARITHMETIC.  141 

4.  If /y  of  the  principal  equals  the  interest,  what  is 
the  rate  per  cent  ? 

5.  K  ¥3_  of  the  principal  equals  the  interest,  what  is 
the  rate  per  cent  ? 

6.  If  ^  of  the  principal  equals  the  interest,  what  is 
the  rate  per  cent  ? 

7.  If  -Jj  of  the  principal  equals  the  interest,  what  is 
the  rate  per  cent  ? 

8.  If  T!y  of  the  principal  equals  the  interest,  what  is 
the  rate  per  cent  ? 

9.  If  Jy  of  the  principal  equals  the  interest,  what  is 
the  rate  per  cent  ? 

10.  If  i  of  the  principal  equals  the  interest,  what  is 
the  rate  per  cent  ? 

11.  B,  by  selling  a  quantity  of  goods,  lost  T£7  of 
what  it  cost ;  what  did  he  lose  per  cent  ? 

12.  A  woman,  by  selling  a  quantity  of  oranges, 
gained  -fj  as  much  as  they  cost  her ;  how  much  did 
she  gain  per  cent  ? 

13.  If  a  merchant,  by  selling  books,  gain  -?-$  of 
what  they  cost ;  how  much  does  he  gain  per  cent  ? 

14.  A  man,  by  selling  a  package  of  books,  gained 
J  of  what  they  cost ;  what  was  his  gain  per  cent  ? 

15.  B,  by  selling  a  hogshead  of  molasses,  gained  £J 
as  many  dollars  as  it  cost  him ;  what  was  his  gain  per 
cent? 

16.  If  by  laying  out  $37,  I  gain  a  sum  equal  to  j 
of  it,  what  do  I  gain  per  cent? 

17.  A  stationer  received  for  a  quantity  of  books,  | 
as  much  as  they  cost  him ;  how  much  did  he  gain  pel 
cent? 

18.  James  received  for  his  horse  J  of  what  it  cost 
him ;  how  much  did  he  gain  per  cent  ? 

19.  A  man  sold  a  barrel  of  pork  for  Ji  of  what  it 
cost  him ;  how  much  did  he  gain  per  cent  ? 

20.  The  interest  on  a  certain  principal  for  4  years, 
was  £  J  of  the  urincipal ;  what  was  the  rate  per  cent  ? 


142  ARITHMETIC. 

REMARK. — If  in  4  years  ||  of  the  principal  equals  the 
.interest,  for  1  year  the  interest  will  be  {  of  £f,  which  is 
j3^  of  the  principal,  &c. 

21.  A  man,  being  asked  what  per  cent  he  received 
on  the  money  he  had  on  interest,  replied,  that  in  10 
years  the   interest  would  equal  |  of  the  principal. 
What  rate  per  cent  did  he  receive  ? 

22.  |  of  the  cost  of  A's  horse,  is  4  times  what  he 
gained  by  selling  it ;  what  was  his  gain  per  cent  ? 

23.  -j\  of  the  money  B  paid  for  silks,  is  twice  what 
he  gained  by  selling  them.     What  did  he  gain  per 
cent? 

24.  y^.  of  the  money  C  paid  for  books,  is  }  of  what 
he  gained  by  selling  them.     How  much  did  he  gain 
per  cent  ? 

25.  -£-s-  of  the  money  I  have  on  interest,  is  4  times 
the  yearly  interest  received.     What  is  the  rate  per 
cent? 

26.  JJ  of  the  cost  of  A's  merchandise,  is  £  of  what 
he  gained  when  he  sold  it.     What  did  he  gain  per 
cent? 

27.  Tj*g-  of  the  cost  of  B's  wagon,  is  J  Of  what  he 
gained  by  selling  it.     What  did  he  gain  per  cent  ? 

28.  A  book  was  sold  for  f  of  £  of  what  it  cost.    What 
was  the  loss  per  cent  ? 

29.  f  of  f  of  the  cost  of  a  sleigh,  was  what  it  was 
sold  for.     What  was  the  gain  per  cent  ? 

30.  A,  being  asked  what  he  gained  per  cent  on  a 
certain  stock  of  goods,  replied,  that  J  of  y  of  what 
they  cost,  equals  what  he  sold  them  for.     What  did 
he  gain  per  cent? 


LESSON    IV. 

1.  At  5  per  cent  for  4  years,  what  part  of  the  prin 
cipal  equals  the  interest  ? 


ARITHMETIC.  143 

SOLUTION  1st.— If  the  interest  on  $1  for  1  year  is  5 
cents,  for  4  years  it  is  4  times  5  cents,  which  are  20  cents. 
If  the  interest  on  100  cents  is  20  cents,  on  1  cent  it  is  T^ 
of  20  cents,  which  is  •$'&  or  J  of  a  cent.  Therefore,  at  5 
^er  cent  for  4  years,  £  of  the  principal  equals  the  interest. 

2.  At  6  per  cent  for  5  years,  what  part  of  the  prin 
cipal  equals  the  interest  ? 

3.  At  3  per  cent  for  2  years,  what  part  of  the 
principal  equals  the  interest  ? 

4.  At  4  per  cent  for  3  years,  what  part  of  the  prin 
cipal  equals  the  interest  ? 

5.  At  6  per  cent  for  3  years,  what  part  of  the 
principal  equals  the  interest? 

6.  At  4  per  cent  for  3  years,  what  part  of  the 
principal  equals  the  interest  ? 

7.  At  9  per  cent  for  6  years,  what  part  of  the  prin 
cipal  equals  the  interest  ? 

8.  At  8  per  cent  for  5  years,  what  part  of  the  prin 
cipal  equals  the  interest  ? 

9.  At  4  per  cent  for  6  years,  what  part  of  the  prin 
cipal  equals  the  interest  ? 

10.  At  6  per  cent  for  8  years,  what  part  of  the 
principal  equals  the  interest  ? 

11.  At  10  per  cent  for  5  years,  what  part  of  the 
principal  equals  the  interest  ? 

12.  At  6  per  cent  for  4  years  and  8  months,  what 
part  of  the  principal  equals  the  interest  ? 


we  will  merely  reier  to  me  lesson  ^ana  give  uie  resuii;  uy  wnicn  a  par- 
Ucular  part  of  the  solution  may  be  performed.  But  the  pupil  must  go 
through  with  the  solution  as  given  in  the  quoted  lesson,  to  obtain  that  re- 
•ult  for  himself. 

SOLUTION  2nd. — We  find  by  Lesson  I.,  that  4  years  and 
8  months  equal  l-f  years.  If  the  interest  on  $1  for  1 
year  is  6  cents,  for  £  of  a  year  it  is  J  of  6  cents,  which  is  2 
cents,  and  for  y  years,  14  times  2  cents,  which  are  28 
cents.  If  on  100  cents  the  interest  is  28  cents,  on  1  cent 
it  is  i-fo  of  28  cents  which  is  ^  ,  or  37j  of  a  cent.  There- 


144  ARITHMETIC. 

fore,  at  6  per  cent  for  4  years  and  8  months  -fg  of  the  priiv 
cipal  equals  the  interest. 

13.  At  4  per  cent  for  6  years  and  6  months,  what 
part  of  the  principal  equals  the  interest  ? 

14.  At  6  per  cent  for  5  years  and  4  months,  what 
part  of  the  principal  equals  the  interest  ? 

15.  At  10i  per  cent  for  1  year  and  6  months,  what 
part  of  the  principal  equals  the  interest  ? 

16.  At  4|  per  cent  for  9  years,  what  part  of  the 
principal  equals  the  interest  ? 

17.  At  3J  per  cent  for  2  years  and  2  months,  what 
part  of  the  principal  equals  the  interest  ? 

18.  At  6£  per  cent  for  4  months  and  24  days,  what 
part  of  the  principal  equals  the  interest  ? 

19.  At  7J  per  cent  for  10  months,  what  part  of  the 
principal  equals  the  interest  ? 

20.  At  3T7V  per  cent  for  2  years  4  months  and  15 
days,  what  part  of  the  principal  equals  the  interest  ? 


LESSON    V. 

1.  What  is  the  interest  of  $50  for  4  years,  at  6  per 
cent? 

SOLUTION. — We  find  by  Lesson  IV.,  that,  -A  of  the  prin 
cipal  equals  the  interest.  ^  of  $50  is  $2,  and  £  is  6  times 
$2.  which  are  $12,  the  required  interest. 

2.  What  is  the  interest  of  $10  for  2  years,  at  5  per 
cent  ? 

3.  What  is  the  interest  of  $48  for  6  years,  at  5  per 
cent? 

4.  What  is  the  interest  of  $70  for  7  years,  at  5  per 
cent? 

5.  What  is  the  interest  of  $68  for  5  years,  at  6  per 
cent? 

6.  What  is  the  interest  of  $70  for  2  years,  at  5  per 
oent? 


ARITHMETIC.  145 

7.  What  is  the  interest  of  $75  for  5  years,  at  3  per 
sent? 

8.  What  is  the  interest  of  $120  for  8  years,  at  5 
per  cent  ? 

9.  What  is  the  interest  of  $100  for  10  years,  at  6 
per  cent  ?  - 

10  What  is  the  interest  of  $140  for  12  years,  at  5 
per  cent  ? 

11.  What  is  the  interest  of  $150  for  5  years,  at  3 
per  cent  ? 

12.  What  is  the  interest  of  $145  for  6  years,  at  5 
per  cent  ? 

13.  What  is  the  interest  of  $200  for  10  years,  at  8 
per  cent  ? 

14.  What  is  the  interest  of  $250  for  3  years,  at  8 
per  cent  ? 

15.  What  is  the  interest  of  $220  for  11  years,  at  10 
per  cent  ? 

16.  What  is  the  interest  of  $500  for  9  years,  at  8 
per  cent  ? 

17.  What  is  the  interest  of  $250  for  12  years,  at  6 
per  cent  ? 

18.  What  is  the  interest  of  $500  for  8  years,  at  12 
per  cent  ? 

19.  What  is  the  interest  of  $200  for  9  years,  at  3 
per  cent  ? 

20.  What  is  the  interest  of  $406  for  10  years,  at  8 
per  cent  ? 

21.  What  is  the  interest  of  $50  for  2  years  and  2 
months,  at  6  per  cent  ? 

REMARK. — We  find  (by  Lesson  I,)  that,  2  years  and  2 
months  equal  y  years.  And,  (by  Lesson  IV.  Solution  2nd.) 
that,  ^  of  the  principal  equals  the  interest,  &c. 

22.  What  is  the  interest  of  $25  for  4  years  and  3 
months,  at  4  per  cent  ? 

23.  What  is  the  interest  of  $80  for  5  years  and  5 
months,  at  6  per  cent  ? 


146  ARITHMETIC. 

24.  What  is  the  interest  of  $60  for  8  years  and  6 
months,  at  6  per  cent  ? 

25.  What  is  the  interest  of  $240  for  3  years  and 
0  months,  at  6  per  cent  ? 

26.  What  is  the  interest  of  $75  for  4  years  and  8 
lonths,  at  9  per  cent  ? 

27.  What  is  the  interest  of  $50  for  2  years  and  9 
months,  at  6  per  cent  ? 

28.  What  is  the  interest  of  $80  for  12  years  and  10 
months,  at  6  per  cent  ? 

29.  What  is  the  interest  of  $69  for  8  years  and  4 
months,  at  2  per  cent  ? 

30.  What  is  the  interest  of  $60  for  4  years  and  8 
months,  at  3  per  cent  ? 

31.  Whatjs  the  interest  of  $600  for  2  years  4 
months  and  15  days,  at  4  per  cent? 

REMARK. — We  find  (by  Lesson  I,)  that,  2  years  4  months 
and  15  days  equal  y  years.  And,  (by  Lesson  IV,  Solution 
2nd,)  that,  -^  of  the  principal  equals  the  interest,  &c. 

32.  What  is  the  interest  of  $300  for  5  years  9 
months  and  18  days,  at  5  per  cent  ? 

33.  What  is  the  interest  of  $550  for  4  years  7 
months  and  6  days,  at  10  per  cent  ? 

34.  What  is   the  interest  of  $500  for  1   year  7 
months  and  18  days,  at  6  per  cent  ? 

35.  What  is  the  interest  of  $250  for  ^  years  7 
months  and  6  days,  at  4  per  cent  ? 

36.  What  is  the  interest  of  $250  f©r  3  years  3 
B.onths  and  6  days,  at  6  per  cent  ? 

37.  What  is  the  interest  of  $50  for  6  years  4  months 
and  24  days,  at  5  per  cent  ? 

38.  What  is  the  interest  of  $75  for  2  years  11 
months  and  6  days,  at  15  per  cent  ? 

39.  What  is  the  interest  of  $150   for  2  years  6 
months  and  12  days,  at  15  per  cent  ? 

40.  What  is  the  interest  of  $300  for  2   years  9 
months  and  18  days,  at  If  per  cent  ? 


ARITHMETIC.  147 


LESSON    VI. 

1 .  What  is  the  amount  of  $75  for  2  years,  ut  6  per 
cent? 

REMARK. — (By  Lesson  IV,)  we  find,  that  -^  of  the  prin 
cipal  equals  the  interest.  The  principal,  which  is  f  f  added 
to  the  interest,  which  is  ^  of  the  principal,  equals  |§  of  the 
principal,  or  the  amount*.  Therefore  ff  of  $75  equals  the 
amount,  &c. 

Those  who  prefer,  can  first  find  the  interest  as  in  the 
preceding  lesson,  to  which  add  the  principal,  and  this  sum 
will  be  the  amount. 

2.  What  is  the  amount  of  $90  for  3  years,  at  7  per 
cent? 

3.  What  is  the  amount  of  $100  for  4  years,  at  5 
per  cent? 

4.  What  is  the  amount  of  $100  Tor  10  years,  at  5 
per  cent  ? 

5.  What  is  the  amount  of  $160  for  8   years,  at  5 
per  cent  ? 

6.  What  is  the  amount  of  $200  for  12   years,  at  5 
pf  r  cent  ? 

7.  What  is  the  amount  of  $210  for  2  years  and  6 
months,  at  4  per  cent  ? 

8.  What  is  the  amount  of  $250  for  4  years  and  3 
months,  at  8  per  cent  ? 

9.  What  is  the  amount  of  $240  for  4  years  and  2 
months,  at  3  per  cent  ? 

10.  What  is  the  amount  of  $500  for  8  years  3 
months  and  6  days,  at  6  per  cent  ? 

11.  What  is  the   amount  of   $200  for  5  years  i 
months  and  24  days,  at  5  per  cent  ? 


LESSON     VII. 

1.  What  principal  will  in  4  years,  at  6  per  cent, 
*ive  $12  interest? 


148  ARITHMETIC. 

SOLUTION. — We  find  (by  Lesson  IV,)  that  -fa  of  the  princi 
pal  equals  the  interest.  And  the  interest  is  $1 2 .  Therefore, 
$12  is  /T  of  the  principal.  If  $12  is  ^  of  the  principal, 
^y  of  tne  principal  is  £  of  $12,  which  is  $2,  and  ||  (the 
principal)  is  25  times  $2,  which  are  $50. 

2.  What  principal  will  in  6  years,  at  4  per  cent, 
give  $36  interest  ? 

3.  What  principal  will  in  4  years,  at  5  per  cent, 
give  $30  interest  ? 

4.  What  principal  will  in  8  years,  at  7  per  cent, 
give  $42  interest  ? 

5.  What  principal  will  in  10  years,  at  7  per  cent, 
give  $140  interest? 

6.  What  principal  will  in  4  years  and  6  months,  at 
6  per  cent,  give  $54  interest  ? 

7.  What  principal  will  in  4  years  and  3  months,  at 
6  per  cent,  give  $102  interest? 

8.  What  principal  will  in  4  years  and  3  months,  at 
8  per  cent,  give  $51  interest  ? 

9.  Ho\v  much  money  has  that  man  on  interest,  who, 
at  the  expiration  of  4  years  and  4  months,  at  6  per 
cent,  receives  $260  interest  ? 

10.  At  the  expiration  of  ?  years  and  4  months,  at 
6  per  cent,  a  man  received  $49  interest.     How  much 
money  had  he  on  interest  ? 

11.  A  is  worth  twice  as  much  as  B,  and  the  in 
terest  of  their   united   fortunes    for  4  years   and   2 
months,  at  6  per  cent,  is  $600.     How  much  is  each 
worth  ? 

12.  The  interest  on  the  cost  of  B's  store  and  house, 
for  1  year  and  6  months,  at  4  per  cent,  would  be  $270. 
What  was  the  cost  of  each,  providing  the  store  cost  | 
as  much  as  the  house  ? 

13.  If  the  money  B  paid  for  a  sheep,  a  cow,  and 
horse,  was  put  on  interest  for  4  years  and  6  months, 
at  4  per  cent^  it  would  give  $18  interest.     What  was 
the  cost  of  al    and  of  each  respectively,  providing  the 


ARITHMETIC.  149 

sheep  cost  £  as  much  as  the  cow,  and  the  cow,  J  as 
much  as  the  horse  ? 


LESSON    VIII. 

1.  What  principal  will  in  4  years,  at  5  per  cent, 
amount  to  $360  ? 

SOLUTION. — We  find  (by  Lesson  IV.)  that  J  of  the  princi 
pal  equals  the  interest.  This  added  to  f  (the  principal) 
equals  f  of  the  principal,  or  the  amount.  If  f  of  the  prin 
cipal  is  $360,  \  is  £  of  $360,  which  is  $60,  and  £  (the 
principal)  is  5  times  $60,  which  are  $300. 

2.  What  principal  will  in  3  years,  at  6  per  cent, 
amount  to  $118? 

3.  What  principal  will  in  6  years,  at  10  per  cent, 
amount  to  $120? 

4.  What  principal  will  in  10  years,  at  7  per  cent, 
amount  to  $170  1 

5.  What  principal  will  in  4  years,  at  5  per  cent, 
amount  to  $660  ? 

6.  A  is  worth  £  as  much  as  B  ;  and  the  interest  on 
their  united  fortunes  for  2  years,  at  5  per  cent,  is 
$880.     What  is  each  of  their  fortunes  ? 

7.  A  merchant  sold  a  quantity  of  cloth  for  $214, 
and  thereby  gained  7  per  cent.     What  did  the  cloth 
cost  him  ? 

8.  What  principal  will  in  2  years,  at  7  per  cent, 
amount  to  $1140? 

9.  What  principal  will  in  10  years  and  8  months, 
at  9  per  cent,  amount  to  $490  ? 

10.  The  amount  due  on  a  note,  which  had  been  on 
interest  6   years  and  2  months,  at  6  per  cent,  was 
$274.     What  was  the  face  of  the  note  ? 

11.  What  principal  will  in  12  years  and  9  months, 
at  4  per  cent,  amount  to  $302  ? 


150  ARITHMETIC. 

12.  If  £  of  A's  fortune  for  4  years  and  6  months,  at 
6  per  cent,  amounts  to  $127 ;  what  is  his  whole  for 
tune  ? 

13.  If  |  of  B's  fortune,  being  put  on  interest  for  3 
years  3  months  and  6  dtys,  at  15  per  cent,  amount 
to  $149  ;  what  is  his  whole  fortune  ? 

14.  A's  fortune  added  to  |  of  B's,  which  is  to  A's 
as  2  to  3,  being  put  on  interest  for  6  years,  at  4 
per  cent,   amounts   to  $124.     What   is   the   fortune 
of  each  ? 

15.  D's   money  added   to  4  times   E's,  which   is 
equal  to  D's,  being  on  interest  for  10  years,  at  5  per 
cent,  amounts   to  $3000.     What  was  each  of  their 
fortunes  ? 

16.  The  sum  of  £  of  A's  +  1  of  B's  money,  being 
on  interest  for  8  years,  at  5  per  cent,   amounts  to 
$2100.     Providing  |  of  B's  money  is  twice  f  of  A's  ; 
how  much  money  has  each  ? 

17.  |  of  the  cost  of  C's  house,  increased  by  J  of  the 
cost  of  his  farm,  being  placed  on  interest  for  10  years, 
at  7   per  cent,  amounts  to  $17000.     What  was  the 
cost  of  each,  if  J  of  the  cost  of  the  house  was  only  J 
of  |  of  the  cost  of  the  farm  ? 

18.  If  ^  of  A's  fortune  in  2  years  and  4  months,  at 
6   per  cent,   amounts   to  $570 ;    what   is  his  whole 
fortune  ? 

19.  The  sum  of  A's,  and  B's  fortune  in  4  years 
and  8  months,  at  6  per  cent,  amounts  to  $256.     What 
Vi'ds  each  of  their  fortunes,  providing  |  of  A's  fortune 

quals  B's  ? 


LESSON    IX. 

1.  In  what  tinv  will  $40,  at  6  per  cent,  give 
interest  ? 


ARITHMETIC.  151 

SOLUTION. — What  part  of  the  principal  equals  the  inter- 
tst?  $1  is  ¥V  °f  tne  principal  and  $12  is  12  times  T^ 
which  are  j[J  or  ^j  of  the  principal.  If  on  1  cent  I  gain 
nr  of  a  cent,  on  100  cents  I  shall  gain  100  times  -^  which 
ire  3^° ,  or  30  per  cent.  If  it  require  1  year  for  $1  to  gain 
&  cents  interest,  to  gain  1  cent,  it  will  require  £  of  a  year, 
and  to  gain  30  cents  it  will  require  30  times  J,  which  aie 
\°  or  5  years. 

2.  In  what  time  will  $60,  at  5  per  cent,  give  $18 
interest  ? 

3.  In  what  time  will  $90,  at  7  per  cent,  give  $27 
interest  ? 

4.  In  what  time  will  $100,  at  6  per  cent,  give  $10 
nterest  ? 

5.  In  what  time  will  $120,  at  10  per  cent,  give 
$120  interest  ? 

6.  In  what  time  will  $250,  at  6  per  cent,  give  $20 
interest  ? 

7.  In  what  time  will  $40,  at  7  per  cent,  give  $8.40 
interest  ? 

8.  In  what  time,  at  8  per  cent,  will  $30  give  $9.60 
interest  ? 

9.  In  what  time,  at  6  per  cent,  will  $10  give  $2.40 
interest  ? 

10.  In  what  time,  at  4  per  cent,  will  $20  give 
$5.60  interest  ? 


LESSON     X. 

1.  At  what  per  cent,  will  $50,  in  1  year  and 
months,  or  (1£  years,)  give  $6  interest  ? 

SOLUTION. — What  part  of  the  principal  equals  the  inter 
est  ?  $1  is  -^  of  the  principal,  and  $6  is  6  times  ^,  which 
ire  ^j-  or  -^  of  the  principal.  If  the  interest  on  1  cent  is 

of  a  cent,  on  100  cents,  it  is  100  times  ^,  which  are 
or  12  cents.  If  in  |  years  the  interest  on  $1  is  12 


152  ARITHMETIC. 

cents,  in  I  of  a  year  it  is  £  of  12  cents,  which  is  4  cents, 
and  in  f  (a  year)  it  is  twice  4  cents,  wh:  ch  are  8  tents,  or 
8  per  cent. 

2.  At  what  per  cent,  will  $40  annually  give  $2 
interest  ? 

3.  At  what  per  cent,  will  $80  annually  give  $3.20 
interest  ? 

4.  At  what  per  cent,  will   $120  annually  give  $12 
interest  1 

5.  At  what  per  cent,  will  $120  in  4  years,  give  $20 
interest  ? 

6.  At  what  per  cent,  will  $100  in  3  years,  give  $30 
interest  ? 

7.  At  what  per  cent,  will  $5  in  14  years,  give  $7 
interest  ? 

8.  At  what  per  cent,  will   $25  in   1   year  and  9 
months,  give  $3.50  interest  ? 

9.  At  what  per  cent,  will  $80  in  5  years  and  8 
months,  give  $34  interest  1 

10.  At  what  per  cent,  will  $500  in  7  years  and  6 
months,  give  $75  interest  ? 

11.  At  what  per  cent,  will  $600  in  2  years  4  months 
and  15  days,  give  $57  interest  ? 


LESSON    XI. 

t 

1.  At  what  per  cent,  will  $10  in  4  years,  amount  to 
12? 

REMARK.— From  the  amount,  subtract  the  principal,  and  the  remainder 
•will  be  the  interest.    Then  proceed  as  in  the  preceding  lesson. 

2.  At  what  per  cent,  will  $12  in  3  years,  amount 
to  $13,44  ? 

3.  At  what  per  cent,  will  $20  in  6  years,  amount 
to  $26  ? 

4.  At  what  per  cent,  will  $24  in  10  years,  amount 
to  $36  ? 


ARITHMETIC.  153 

5.  At  what  per  cent,  will  $30  in  7  years,  amount 
to  $36.30  ? 

6.  At  what  per  cent,  will  $50  in  10  years,  amount 
to  $75  ? 

7.  At  what  per  cent,  will  $36  in  5  years,  amount 
to  $39.60  ? 

8.  At  what  per  cent,  will  a  given  principal  double 
itself,  in  20  years  ? 

SOLUTION. — A  given  principal  will  double  itself  in  1  year, 
at  100  per  cent;  and  in  20  years,  at  ^  of  100  per  cent, 
which  is  5  per  cent  ? 

9.  At  what  per  cent,  will  a  given  principal  double 
itself,  in  4  years  ? 

10.  At  what  percent,  will  a  given  principal  double 
itself,  in  3  years  ? 

11.  At  what  per  cent,  will  a  given  principal  double 
itself,  in  5  years  ? 

12.  At  what  per  cent,  will  a  given  principal  double 
itself,  in  7  years  ? 

13.  At  what  per  cent,  will  a  given  principal  double 
itself,  in  6  years  ? 

14.  At  what  percent,  will  a  given  principal  double 
itself,  in  8  years  ? 

15.  At  what  per  cent,  will  a  given  principal  double 
itself,  in  9  years  ? 

16.  At  what  per  cent,  will  a  given  principal  double 
itself,  in  25  years  ? 

17.  At  what  per  cent,  will  a  given  principal  double 
itself,  in  30  years  ? 

18.  At  what  per  cent,  will  a  given  principal  double 
itself,  in  12|  years  ? 

19.  At  what  per  cent,  will  a  given  principal  double 
itself,  in  14|  years  ? 

20.  At  what  per  cent,  will  a  given  principal  double 
itself,  in  31f  years  ? 


164  ARITHMETIC. 


LESSON    XII. 

1.  In  what  time  will  a  given  principal  double  itself, 
at  5  per  cent  ? 

SOLUTION. — A  given  principal  will  double  itself  in  100 
years  at  1  per  cent,  and  at  5  per  cent,  in  J  of  100  years, 
which  is  20  years. 

2.  In  what  time  will  a  given  principal  double  itself, 
at  4  per  cent  ? 

3.  In  what  time  will  a  given  principal  double  itself, 
at  3  per  cent  ? 

4.  In  what  time  will  a  given  principal  double  itself, 
at  6  per  cent  ? 

5.  In  what  time  will  a  given  principal  double  itself, 
at  2  per  cent  ? 

6.  In  what  time  will  a  given  principal  double  itself, 
at  7  per  cent  ? 

7.  In  what  time  will  a  given  principal  double  itself, 
at  9  per  cent  ? 

8.  In  what  time  will  a  given  principal  double  itself, 
at  8  per  cent  ? 

9.  In  what  time  will  a  given  principal  double  itself, 
at  10  per  cent  ? 

10.  In  what  time  will  a  given  principal  double  itself, 
at  12  per  cent  ? 


LESSON    XIII. 

1.  Bought  a  bushel  of  grass-seed,  for  $5  and  sold  it 
br  $7  ;  what  was  the  gain  per  cent  ? 

SOLUTION. — Since  it  was  bought  for  $5  and  sold  for  $7, 
the  gain  must  have  been  $7  —  $5,  which  is  $2.  If  on  $5 
the  gain  is  $2,  on  $1  it  will  be  f  of  a  dollar,  (or  J  of  a  cent 
on  1  cent). 

If  the  gain  on  1  cent  is  f  of  a  cent,  on  100  cents,  it  it 
100  times  f  of  a  cent,  which  are  *J°  or  40  per  cent. 


ABTTHMETIC. 


155 


2.  A  book  was  bought  for  $2,  and  sold  for  $3 ; 
what  was  the  gain  per  cent  ? 

"  3.  A  shawl  cost  $5,  and  was  sold  for  $8 ;  what 
was  the  gain  per  cent  ? 

4.  A  cow  was  bought  for  $20,  and  sold  for  $25; 
what  was  the  gain  per  cent  ? 

5.  A  merchant  bought  a  hogshead  of  molasses  for 
$80,    and  sold  it  for  $95;    what  did  he  gain   per 
cent? 

6.  A  barrel  of  pork  cost  $12,  and  was  sold   for 
$11 ;  what  was  the  loss  per  cent  ? 

7.  A  horse  was  bought  for  $140,  and  sold  for  $60 ; 
what  was  the  loss  per  cent ? 

8.  Bought  an  orange  for  4  cents,  and  sold  it  for  6 
cents  ;  what  was  the  gain  per  cent  ? 

9.  Bought  a  melon  for  15  cents,  and  sold  it  for  20 
cent? ;  what  was  the  gain  per  cent  ? 

10.  Bought  a  book   for  5  dimes,  and  sold  it  for  8 
dimes ;  what  was  the  gain  per  cent  ? 

11.  Bought  a  quantity  of  silk  for  $120,  and  sold  it 
for  $200  ;  what  was  the  gain  per  cent  ? 

12.  A   boy  sold  melons,  at  the  rale  of  10  cents 
apiece,   J  of  which  equaled  his  gain  ;    how  much 
would  he  have  gained  per  cent,  if  he  had  sold  them, 
at  12  cents  apiece  ? 

13.  A  merchant  sold  sugar,  for  $80  a  hogshead, 
and  thereby  cleared  TT¥  of  this  money  ;  if  he  had  sold 
it,  at  $92  a  hogshead ,  what  would  he  have  gained 
per  cent  ? 

14.  A  quantity  of  cloth  was  bought  for  $36,  and 
soid  for  $43  ;  what  was  the  gain  per  cent  ? 

15.  A  horse  was  bought  for  $100,  and  sold  for  $95 ; 
arhat  was  the  loss  per  cent  1 


156  ARITHMETIC. 

LESSON    XIV. 

1.  A  man  bought  a  cow  for  $20  ;  for  what  must 
he  sell  her,  to  gain  5  per  cent  on  the  cost  ? 

SOLUTION. — If  he  gains  5  cents  on  100  cents,  on  1  cent 
be  will  gain  j-J-jj-  of  5  cents,  which  is  yl^,  or  •£$  of  a  cent. 
Consequently  he  must  sell  it  for  f  £  of  what  it  costs,  &c. 

2.  A  man  bought  a  yoke  of  oxen   for  $100 ;    how 
must  he  sell  them,  to  gain  6  per  cent  on  the  cost  ? 

3.  A  man  bought  a  barrel  of  rum  for    $10 ;   for 
what  must  he  sell  it,  to  gain   10  per  cent  on  the 
cost? 

4.  A  gallon  of  wine  was  bought  for  20  dimes  ;  how 
must  it  be  sold  a  pint,  to  gain  20  per  cent  on  the 
cost? 

5.  A  hogshead  of  molasses  cost  $20  ;    for  what 
ought  it  to  be  sold  a  gallon,  to  gain  40  per  cent  on  the 
cost? 

6.  B  bought  a  horse  for  $80,  and  by  seV  .ng  it,  lost 
5  per  cent  on  the  cost ;  for  what  did  he  se\i  it  ? 

7.  A  wagon  cost    $140  dollars,  and  was  sold   for 
5  per  cent  less  than  it  cost ;  for  what  was  it  sold  ? 

8.  A   merchant,  by  selling  40  yards  of  cloth   for 
$164,  lost  20  per  cent  on  the  cost.     What  did  it  cost 
per  yard  ? 

9.  If  a  quart  of  brandy  cost  50  cents,  how  must 
it  be  sold  a  gill,  to  lose  4  per  cent  ? 

1A.  B  lost  5  per  cent,  by  selling  a  gallon  of  rum, 
which  cost  80  cents ;  for  what  did  he  sell  it  a  gallor  I 


LESSON    XV. 

1.  What  principal  will,  in  4  years,  at  5  per  cent, 
amount  to  $60  ? 


ARITHMETIC.  157 

SOLUTION. — We  find  (by  Lesson  IV,)  that  ^  of  the  princi 
pal  equals  the  interest,  £  (the  principal)  and  J  (the  inter 
est)  added,  is  f  of  the  principal,  which  equals  the  amount. 
If  |  of  the  principal  is  $60,  }  is  J  of  $60,  which  is  $10 ;  and 
f,  (the  principal,)  is  5  times  $10,  which  are  $50. 

2.  What  principal  will,  in  3  years,  at  6  per  cent, 
amount  to  $118  ? 

3.  What  principal  will,  in  5  years,  at  6  per  cent, 
amount  to  $130  ? 

4.  What  principal  will,  in  7  years,  at  5  per  cent, 
amount  to  $81  ? 

5.  What  principal  will,  in  9  years,  at  8  per  cent, 
amount  to  $86  ? 

6.  What  principal  will,  in  3J  years,  at  8  per  cent, 
amount  to  $260  ? 

7.  What  principal  will,  in  4|  years,  at  6  per  cent, 
amount  to  $640  ? 

8.  What  principal  will,  in  5|  years,  at  7  per  cent, 
amount  to  $42  ? 

9.  What  principal  will,  in  6f  years,  at  7  per  cent, 
amount  to  $87  ? 

10.  What  principal  will,  in  8|  years,  at  6  per  cent, 
amount  to  $76  1 


time,  and  rate  per  cent. 
See  the  above  solution. 


11.  What  is  the  present  worth  of  $26,  due  5  yeart 
hence,  at  6  per  cent  ?  Ans.  $20. 

12.  What  is  the  present  worth  of  $14,  due  8  years 
hence,  at  5  per  cent  ? 

13.  What  is  the  present  worth  of  $110,  due  5  years 
hence,  at  5  per  cent  ? 

14.  What  is  the  present  worth  of  $86,  due  8  years 
hence,  at  9  per  cent  ? 


158  ARITHMETIC. 

15.  What  is  the  present  worth  of  $102,  due  9  years 
hence,  at  4  per  cent  ? 

16.  What  is  the  present  worth  of  $72,  due  4  years 
hence,  at  5  per  cent  ? 

17.  What  is  the  discount  on  $46,  due  3  years  hence, 
t  5  per  cent  ? 

REMARK. — The  discount  equals  the  amount  minut  the  present  worth. 

18.  What  is  the  discount  of  $54,  due  5  yeans  hence, 
at  7  per  cent  ? 

19.  What  is  the  discount  of  $65,  due  5  years  hence, 
at  6  per  cent  ? 

20.  What  is  the  discount  of  $93,  due  3  years  hence, 
at  8  per  cent  ? 

21.  What  is  the  present  worth    of  $186,  due  4f 
years  hence,  at  5  per  cent  ? 

22.  What  is   the    present  worth    of  $66,  due  5* 
years  hence,  at  6  per  cent  ? 

23.  What   is  the   present  worth  0f  $128,  due  4J 
years  hence,  at  6  per  cent  ? 


LESSON    XVI. 

1.  If  I  sell  cloth,  at  $2.50  a  yard,  and  thereby  gain 
25  per  cent ;  what  did  it  cost  a  yard  ? 

SOLUTION. — 25  per  cent  is  j  of  the  cost  (Lesson  II.)  | 
(the  cost)  -f-  I  (the  gain)  is  |  of  what  it  cost  me,  which 
equals  what  I  sold  it  for.  If  |  of  what  I  gave  for  it,  is 
$2.50,  I  is  }  of  $2.50,  which  is.50  cents;  and  £  (the  cost) 
is  4  times  50  cents,  which  are  200  cents,  ($2.) 

2.  A  horse  was  sold   for  $38,  which  was   at  a  loss 
of  5  per  cent.     What  did  the  horse  cost  ? 

3.  If  I  sell  cloth,  at  $2.50  a  yard,  and  thereby  gain 
25  per  cent,  how  must  I  sell  it  a  yard,  to  lose  20  per 
cent  ? 

4.  If  I  sell  cloth,  at  $4.40  a  yard,  and  thereby  gain 
10  per  cent,  hov  ought  I  to  sell  it,  to  lose  25  per  cent  ? 


ARITHMETIC.  159 

5.  If  by  selling  a  piece  of  cloth  for  $46,  I  gain  15 
per  cem,  how  ought  1  to  have  sold  it,  to  have  lost  30 
per  cent  ? 

6.  A  sold  his  horse  for  $105,  and  thereby  gained  5 
per  cent  on  the  cost ;  for  what  ought  he  to  have  sold 
it,  to  have  lost  10  per  cent  ? 

7.  A  farm  was  sold  for  $495,  which  was  10  per  cent 
less  than   what  it  was  worth  ;  for  what  ought  it  to 
have  been  sold,  to  have  received  40  per  cent  more 
than  its  value  ? 

8.  A  mechanic  lost  20  per  cent  on  the  cost  of  a 
wagon,  by  selling  it  for  840  ;  for  what  ought  it  to 
have  been  sold,  to  have  gained  30  per  cent  ? 

9.  A  horse  was  sold  for  $90,  which  was  10  per 
cent  less  than  its  value ;  what  would  have  been  the 
gain  per  cent,  if  it  had  been  sold  for  $120  ? 

10.  A  farm  was  sold  for   $690,  which  was  8  per 
cent  less  than  its  value  ;  what  would  have  been  the 
gain  per  cent,  if  it  had  been  sold  for  $850  ? 

11.  A  book  was  sold  for  90  cents,  which  was  10 
per  cent  less  than  its  value  ;  what  would  have  been 
the  gain  per  cent,  if  it  had  been  sold  for  $1.50  ? 

12.  A  man  sold  two  watches,  at  $12  each  ;  on  one 
he  gained  50  per  cent,  and  on  the  other  he  lost  50  per 
cent.     Did  he  gain  or  lose  by  the  bargain,  and  how 
much  ? 

13.  An  individual  sold  two    gold    pencils,  at   $6 
apiece ;  on  one  he  gained  20  per  cent,  and  on  the  other 
he  lost  20  per  cent  Did  he  gain  or  lose,  and  how  much  ? 

14.  A  farmer  sold  two  horses  at  $210  apiece  ;  for 
one  he  received  25  per  cent  more  than  its  value,  and 
for  the  other  25  per  cent  less  than  its  value.     Did  he 
gain  or  lose  by  the  bargain,  and  how  much  ? 

15.  A   merchant  sold  a  quantity  of  cloth  for  $80, 
and  by  so  doing  lost  60  per  cent ;  he  then  sold  another 
quantity  for  $80,  and   thereby  gained   60  per  cent. 
Did  he  gain  or  lose  by  the  operation  and  how  much  ? 


160  ARITHMETIC. 


LESSON    XVII. 

1.  An  individual  was  ordered  to  collect  $190,  and 
was  to  receive  5  per  cent  on  all  the  money  collected. 
How  much  should  he  receive  ? 

REMARK.— It  will  be  understood  that  he  is  to  collect  his  own  fee,  and 
tfiust  receive  5  per  cent  on  that  also. 

SOLUTION. — We  find  (by  Lesson  II.)  that  he  is  to  receive 
SV  of  all  he  collects.  Therefore  f£,  (what  he  collects) — 
5^  (his  fee)  is  J|  of  what  he  collects,  which  is  $190,  (the 
sum  to  be  paid  to  his  employer.)  If  ^f  of  what  he  collects 
equals  $190,  ^  is  f\  of  $190,  which  is  $10 ;  andjg  (what 
he  collects)  is  20  times  $10,  which  are  $200.  Therefore 
he  must  receive  $200  —  $190  =  $10. 

2.  What  ought  A  to  receive  for  collecting  $90,  if  he 
receive  10  per  cent  on  all  he  collects  ? 

3.  What  amount  of  money  will  be  sufficient  to  pay 
a  debt  of  $38  and  the  collector's  fee,  which  is  5  per 
cent  on  all  the  money  collected  ? 

4.  How  much  cider  must  that  man  make  to  fetch 
away  15  barrels,  after  the  owner  of  the  mill  receives 
16|  per  cent  of  all  he  has  made  ? 

5.  How   much   grain   must  a  farmer  take  to  mill, 
that  he  rcay  bring  away  the  flour  of  1  bushel,  after  the 
miller  has  taken  10  per  cent,  of  all  he  took  there  ? 


MISCELLANEOUS   EXAMPLES. 

1.  At  5  per  cent  for  4  years,  what  part  of  the  prin 
cipal  equals  the  interest  1 

2.  In  how  many  years,  at  4  per  cent,  will  a  given 
principal  amount  to  the  same,  as  it  would  in  8  years, 
at  6  per  cent  ? 

3.  At  what  per  cent  will  a  given  principal,  in  14 
years,  amount  to  the  same,  as  it  would  in  12  years, 
at  7  per  cent  ? 


ARITHMETIC.  161 

4.  If  /y  of  the  principal  equals  the  interest,  what  is 
the  rate  per  cent  ? 

5.  The  rent  of  B's  farm,  for  8  years  amounted  to 
|f  of  its   value.     What   per  cent  did   he  annually 
receive  on  the  value  of  his  farm  ? 

6.  What  is  the  interest  of  $75,  for  5J  years,  at 
per  cent  ? 

7.  What  principal  will,  in  7£  years,  at  8  per  cent, 
give  $24  interest  ? 

8.  What  principal  will,  in  4J  years,  at  5  per  cent, 
amount  to  $155  ? 

9.  At  what  per  cent,  will  a  given  principal  double 
itself,  in  12J  years? 

10.  The  interest  of  A's,  and   B's   fortune,  for   9 
years,  at  5  per  cent,  is  $420.     What  is  the  fortune  of 
each,  providing  A's  fortune  is  twice  B's  ? 

1 1 .  The  interest  of  f  of  A's  and  £  of  B's  fortune,  for 
7  years,  at  5  per  cent,  is  $2100.     What  is  each  of  their 
fortunes,  providing  f  of  A's  fortune  equals  £  of  B's  ? 

12.  B  sold  his  horse,  for  1  of  1£  times  what  it  cost ; 
what  did  he  lose  per  cent  ? 

13.  What  is  the  interest  of  $540,  for  4  years,  at  5 
per  cent  ? 

14.  What  is  the  interest  of  $180,  for  5  years  and  9 
mon-ths,  at  6|  per  cent  ? 

15.  What  principal  will,  in  4  years  7  months  and 
3  days,  at  6£  per  cent,  amount  to  $412  ? 

16.  The  interest  of  the  cost  of  B's  horse,  sleigh  and 
wagon,  for  6  years,  at  5  per  cent,  is  $69.     What  is 
the  cost  of  each,  providing  their  prices  are  to  each 
other  respectively,  as  J,  f  and  £  ? 

17.  What  principal  will,  in  8  years  and  8  months, 
at  7J  per  cent,  amount  to  $419  ? 

18.  What  principal  will,  in  5  years  9  months  and 
18  days,  at  10  per  cent,  give  $116  interest  ? 

19.  In  what  time,  will  $420,  at  5  per  cent,  give 
$147  interest? 


162  ARITHMETIC. 

20.  If  the  interest  of  $200,  for   1  year  and  6 

months,  is  $18,  what  is  the  rate  per  cent  ? 

21.  At  what  per  cent,  will  $500,  in  4  years  and  9 
months,  give  $190  interest? 

22.  At  what  per  cent,  will  $500,  in  22  years  and 
6  days,  amount  to  $1821  ? 

23.  At  what  per  cent  will  a  given  principal  double 
itself,  in  20  years  ? 

24.  In  what  time  will  a  given  principal  double  it 
self,  at  124-  per  cent  ? 

25.  At  what  per  cent  will  a  given  principal  double 
itself,  in  6  years  and  8  months  ? 

26.  A  horse  was  bought  for  $60,  and  sold  for  $90  ; 
what  was  the  gain  per  cent  ? 

27.  A  basket  containing  39  oranges,  cost  $1.20; 
how  must  they -be  sold  apiece  to  gain  30  per  cent  ? 

28.  If  1  quart  of  champagne  cost  40  cents,  how 
must  it  be  sold  a  gill  to  gain  20  per  cent  ? 

29.  What   is  the   present  worth  of  $68,  due  10 
years  hence,  at  7  per  cent  ? 

30.  What  is  the  discount  on  $162,  due  10  years 
and  4  months  hence,  at  6  per  cent  ? 

31.  What  is  the   present  worth  of  $87,  due  3£ 
years  hence,  at  5  per  cent  ? 

32.  If  a  hogshead  of  molasses  containing  84  gal 
lons  cost  $30,  how  must  it  be  sold  a  gallon,  to  gain 
40  per  cent  ? 

33.  The  money  I  have  on  interest,  in  9  years,  at 
10  per  cent,  amounts  to  $190  ;  what  is  the  princi 
pal  ? 

34.  When  money  was  worth  6  per  cent,  I  bought 
$400  worth  of  goods  ;  6  months  afterwards  I  sold 
them,  and   gained    10  per  cent  on  the  cost.     How 
much  did  I  gain  ?  Ans.  $28. 

35.  A  speculator  bought  a  horse   for  $36,  and 
sold   it  for  25  per  cent  more  than  he  gave  for  it ; 
which,  however,  was    10   per  cent  less  than  what 


ARITHMETIC.  163 

he  asked  for   it.      How  much   did  he   ask  for   the 
borse  ? 

36.  A  gentleman  being  asked  how  much  money  he 
had  on  interest,  replied,  that  if  instead  of  6  per  <jerit. 
he  should  receive  10  per  cent.,  he  would  receive  $268 
interest  more  than  he   then  did.     How  much  money, 
had  he  on  interest  ? 

37.  A  merchant  bought  broadcloth  for  $1.20  a  yard 
and  sold  it  for  33J  per  cent,  more  than  he  gave  for  it; 
which,  however,  was  33}  per  cent,  less  than  his  marked 
price  for  it.     How  much  was  his  marked  price   per  *~ 
yard  ? 

38.  A  merchant  sold  a  quantity  of  cloth  for  $120, 
and  by  so  doing,  gained  50  per  cent.     He  then  sold 
another  quantity,  for    $120,  arid  thereby  lost  50  per 
cent.     Did  he  gain  or  lose   by  the  bargain,  and  how 
much  ? 

39.  B  sold  a  horse  for  $60,  and  gained  20  per  cent. 
He  then  sold  another  horse  for  $60,  and  lost  60  per 
cent.     Did  he  gain  or  lose,  and  how  much  ? 

40.  The  interest  on  1£  times  A's,  and  f  of  B's  for 
tune,  for  8  years,  at  5  per  cent,  is   $520.     What  is 
the  fortune  of  each,  providing   1 £   times  A's  fortune, 
equals  f  of  B's  ? 

41.  f  of  D's  fortune  added  to  £  of  E's,  which  is  3 
times  |  of  D's,  being  put  on  interest  for  8  years,  at  5 
per  cent,  gives  $800  interest.     What   is  the  fortune 
of  each  ? 

42.  The  interest  of  A's,  B's,  and  C's  fortune,  for 
5  years,  at  8  per  cent,   is   $1040.     What  is  the  for 
tune  of  each,  providing  they  are   to  each  other  as  £, 
i,andi? 

43.  The  interest  of  A's,  B's,  and  C's  fortune,  for 
5|  years,  at  6  per  cent,  is  $800.     What  is  each  of 
their  fortunes,  providing  B's,  is  twice  A's;  and  B^, 
and  C's,  are  equal  ? 

44.  The  interest  of  the  sum  of  £  of  A's,  and  f  of 


164  ARITHMETIC. 

B's  fortune,  for  a  certain  time,  at  2  per  cent,  was  to 
this  sum  as  9  to  250.  And  the  amount  of  this  interest 
for  25  times  as  long,  at  10  times  as  great  a  per  cent 
was  $180.  What  was  each  of  their  fortunes,  providing 
A's  fortune  was  to  B's  as  1  to  3  ?  And  how  long  was 
the  first  on  interest  ? 

REMARK. — Since  the  interest  was  to  the  principal  as  C 
to  250,  2  Iff  °f  tne  principal  equals  the  interest.  By  Lessen 
IX,  this-readily  gives  1  year  9  months  and  18  days  for  the 
required  time. — By  the  first  condition  of  the  question  231 
of  the  principal  equals  the  interest;  and  for  25  times  a* 
long,  at  10  times  as  great  a  per  cent,  the  interest  would 
bo  9  times  the  principal ;  which  added  to  1  (the  princi 
pal)  is  10  times  the  principal  (the  first  interest,)  whiel 
equals  $180  (the  amount.)  Therefore  $18  was  the  prin 
cipal  (the  first  interest,)  which  equaled  ^f^  of  the  first 
principal,  which  we  readily  find  to  be  $500,  which  is  the 
sum  of  |  of  A's  and  f  of  B's  fortune.  And,  since  A's  for 
tune  was  to  B's  as  1  to  3,  we  easily  find  that  f  of  B's  for 
tune  equals  4  times  £  of  A's.  Consequently  ]  of  $500  was 
?  of  A's  fortune,  and  J  of  $500  was  f  of  B's.  Therefore, 
A's  fortune  was  $200,  and  B's  $600. 


RECOMMENDATIONS 


From  the  State  of  New  York. 

Secretary's  Office,  ALBANY,  Dec.  15,  1849.  Dtp.  of  Com.  Schtolt 
I  have  examined  "Stoddard's  American  Intellectual  Arithmetic."1, 
and  cheerfully  recommend  it  to  Teachers  and  Parents,  as  a  valuabit 
elementary  work,  and  one  weR  adapted  to  the  wants  of  pupils  in  the 
first  stages  of  Arithmetic.  It  is  constructed  upon  sound  and  practical 
principles,  and  will  be  found  an  important  addition  to  the  text-book* 
BOW  in  use  in  our  Common  Schools. 

SAMUEL  S.  RANDALL, 
Deputy  Sup't.  Common  Schools. 


GENEVA,  N.  Y.,  Oct.  8th,  1850. 

Having  examined  "Stoddard's  Intellectual  Arithmetic,"  I  am  satisfied 
it  is  a  work  of  superior  merit,  and  have  concluded  to  introduce  it  into 
our  school. 

J.  SWIFT, 
Principal  of  Geneva  Union  School. 


FROM  ELMIRA. 

From  a  knowledge  of  the  success  of  teaching  from  John  F.  Stoddard'ff 
"American  Intellectual  Arithmetic,"  in  the  New  York  State  Normal 
School,  and  the  Albany  Male  Academy,  under  the  charge  of  the  Rev. 
Dr.  Campbell,  I  have  no  hesitation  in  saying  that  it  is  EMINENTLY  SUPE 
RIOR  TO  COLBURN'S  Mental  Arithmetic.  To  speak  of  all  its  peculiar  merits 
I  deem  wholly  unnecessary  on  the  present  occasion  ;  but  would  simply 
remark,  that  it  is  more  Elementary  than  Colburn's,  and  embraces  a  sim 
plification  of  all  the  rules  of  common  Arithmetic,  as  well  as  many  of  the 
more  abstruse  principles  of  the  higher  Mathematics.  I  have  purchased 
a  supply  for  introduction. 

A.  R.  WRIGHT,  Principal. 

Slmiia  Union  School,  No  2  ;  Sept.  18,  1850. 

FROM  BUFFALO. 

The  undersigned  Principals  of  Public  Schools  in  the  city  of  Buffalo, 
K.  Y., — (tne  former  having  carefully  examined,  and  the  latter  having 
thoroughly  tested  in  his  School-Room,) — "Stoddard's  Intellectual  Arith 
metic,"  take  pleasure  in  saying  that  it  is  superior  to  Colburn's,  for  tha 
following  reasons  :  It  is  systematically  and  Philosophically  arranged, 
contains  a  much  greater  variety  of  Classes  of  Practical  Examples,  is 
adapted  to  the  currency  of  our  country,  embraces  an  m~iginal  and  very  im 
portant  chapter  on  the  subject  of  Interest,  Discount,  and  Per-Cent., 
and  avoids  those  sudden  changes  from  simple  to  complex  Examples, 
which  is  the  most  objectionable  feature  in  Colburn's  ;  and  withal,  is 
published  im  &  superior  style. 

J.  A.  DOLE,  Principal  of  No.  1, 

and  Pres't.  of  Buffalo  Teachers  Association. 
W.  W.  NEWMAN,  Principal  of  No.  13, 

and  Sec'y,  of  P.mTalo  Teachers  Association. 


RECOMMENDATIONS. 

LIBERTY,  N.  T.,  Jfcn.  lit,  18*0. 

Ut  Stcddard  is  a  practical  teacher  and  his  "American  Intellectual 
iv*i'4-n*lic"  is  the  result  of  much  lalor,  and  its  publication  was  aug- 
jTisrtHj  by  its  great  advantages  in  his  t  wn  experience  as  an  Instructor. 

I  hfve  examined  the  work  with  considerable  care,  and  great  pleasure  * 
lud  I  havo  no  hesitation  in  saying  that  it  is  admirably  adapted  to  pro 
.note  mental  discipline,  and  the  study  of  numbers,  both  in  their  simplt 
and  more  complicated  forms.  The  arrangement  is  so  natural,  and  th« 
transition  from  the  most  simple  to  the  most  abstruse  questions  so  e&sy 
»nd  gradual  (I  might  say  imperceptible),  that  the  difficulties  of  Arith 
metic  have  vanished,  and  habits  of  mental  exertion  are  formed  befoj* 
the  pupil  is  aware  of  it.  I  am  happy  to  learn  that  the  book  is  already 
extensively  introduced  into  schools,  as  a  standard  text-book.  From  its 
superiority  to  any  of  the  same  kind,  with  which  I  am  acquainted,  and 
having  personally  observed  the  astonishing  progress  made  by  those  who 
have  studied  it  under  Mr.  Stoddard's  own  training,  I  can  with  the  ut« 
most  confidence  recommend  it  as  a  class-book,  to  all  who  have  the  in 
struction  of  children  and  youth  in  schools  or  academies. 

JAMES  PETIUE,  A.  M., 
Professor  of  Languages  in  Liberty  Normal  Institute. 


Extract  from  fJie  Report  of  the  Committee  on  Text-Books  of  the  Onorflaga 
County  Teachers  Institute.     Adopted  Jlpril,  1850. 

"Coiourn's  Mental  Arithmetic"  is  generally  considered  an  original 
tnd  standard  work  ;  indeed,  almost  beyond  the  hope  of  competition  or 
Improvement.  The  late  DAVID  P.  PAOK,  says  of  it,  "Colburn's  was  the 
first,  arid  it  is  probably  the  best  that  has  been  prepared.  That  little 
book  has  done  more  than  any  other  for  the  improvement  of  teaching  in 
this  country."  Mr.  Page,  however,  often  spoke  of  its  imperfections, 
and  intended  to  prepare  a  work  himself  on  this  subject.  Hia  sudden 
death  deprived  the  public  of  that  important  educational  auxiliary  ;  but 
a  volume  has  been  prepared  by  .Mr.  John  F.  Stoddard,  a  graduate  of  the 
New  York  State  Normal  School,  which  your  Committee  venture  to  re- 
commend  to  be  substituted  for  Colburn  in  all  our  schools.  Two  of  yeu/ 
Committee,  some  months  since,  became  se  favorably  impressed  by  an 
examination  of  this  work,  as  to  try  the  experiment  of  its  use  in  their 
schools  ;  and  they  very  freely  say,  that  though  Colburn'a  has  long  been 
with  them  a  favorite  and  much-used  volume,  they  are  fc.*y  satisfied,  by 
trial  in  the  school-room,  that  Stoddard's  is  very  much  its  superior. 

Of  Colburn's  work,  we  will  briefly  say,  that  it  is  not  sufficiently 
gradual  and  systematic  :  there  are  too  many  important  omissions  ;  too 
many  sudden  transitions  from  examples  that  are  very  easy,  to  those  thai 
are  very  difficult  :  it  is  not  sufficiently  extended  in  some  parts  :  it  is  nol 
well  ad'apted  to  the  currency  of  our  country,  and  there  is  not  an  appro 
priate  variety  of  classes  of  questions.  These  deficiencies,  we  believe, 
are  obviated  by  the  labors  of  Mr.  Stoddard.  The  first  half  of  his  book  is 
en  a  similar,  but  improved  plan  of  Colburn's.  Some  portions  of  the  last 
half  are  much  more  difficult  than  Colburns  ;  and  it  includes  many 
classes  of  examples,  not  introduced  into  any  other  mental  arithmetic  yet 
published.  It  embraces  sonu-  fifty  pages  of  examples  suitable  for  alge 
braic  as  well  as  arithmetical  solutions,  and  about  the  same  amount  on 
per  ceritage,  in  all  its  variations,  on  an  entirely  new  system,  and  of  an 
original,  philosophic,  and  prac.ical  application.  These  two  portions,  at 
least  for  advanced  pupils,  we  think  entitle  "Stoddard'a  American  Intel* 
iDctual  Arithmetic"  to  a  more  favorable  consideration  than  any  other 
work  now  before  tUs  public  ;  and  we  therefore  cordially  commend 


RECOMMENDATIONS. 

It  to  th«  farorable  notice  of  our  teachers,  confidently  believing,  that 
iti  superior  merits  will  ultimately  banish  the  very  popular,  though  fat 
rrom  being  perfect,  work  of  Colburn  from  all  our  schools. 

JAMES  JOHONNOT, 

H.  G.  McGONEGAL, 

A.  BRADBURV, 

E  C.    PALMER, 
Report  and  Book  were  adopted  by  the  Institute. 

Vsttrs.  Ccrniih,  Lamport  «f-  Co.  : 

GENTS  :— I  have,  with  considerable  care,  examined  a  copy  of  th« 
*  American  Intellectual  Arithmetic,"  by  John  F.  Stoddard,  and  take 
pleasure  in  announcing  that  I  regard  it  as  superior  to  any  other  work  of 
the  k^.nd  with  which  I  am  acquainted.  I  think  it  excels  both  Colburn'i 
and  Thompson's  Mental  Arithmetic,  in  presenting  as  it  does,  all  their 
simplicity,  and  at  the  same  time,  a  more  systematic  and  extended  view 
of  mental  operation.!.  It  is  eminently  calculated  to  invigorate  and  de 
velop  the  reasoning  faculties,  and  prepare  the  pupil  to  acquire,  compara 
tively  with  ease,  a  thorough  knowledge  of  mathematics. 

WM.  HUMPHREY, 
1st  Assistant  Teacher  in  the  Union  School,  Geneva,  N.  Y 

October   1850 


MIDDLE-TOWN,  N.  Y.,  Aug  26,  1850. 

GKITTB  : — Having  examined  "Stoddard's  Juvenile  and  Intellectual 
Arithmetics,"  I  freely  state  that  I  deem  them  the  best  series  of  the  kind 
I  have  ever  met  with,  and  well  adapted  to  properly  discipline  and 
develop  the  minds  of  pupils.  I  have  already  introduced  them  in  the 
schools  of  this  village  and  in  the  Wallkill  Academy,  and,  as  oppor 
tunity  presents,  will  introduce  them  in  the  schools  throughout  the 

Yours,  &c.  H.  EVERETT, 

Town  Superintendent 


PORT  JARVIS..N.  Y.,  Aug.  27th,  1850. 

From  a  careful  examination  given  to  "Stoddard's  Introductory  Les 
sons  and  Mental  Exercises  in  Intellectual  Arithmetic,"  1  feel  assured 
that  the  public  are  under  obligations  to  the  Author,  for  the  happy  man 
ner  in  which  he  has  graduated  the  science  to  the  capacity  of  the  juveniln 
mind. 

Mr.  Stoddard  seems  to  keep  simplicity  in  view,  and  at  the  same  timt 
aims  to  enable  the  Student  to  arrive  at  a  thorough  understanding  of  this 
most  indispensible  Science.  I  have  purchased  a  quantity  of  the  Arith 
metics  from  your  Agent,  for  immediate  introduction  into  the  schools  of 
this  town. 

Yours  truly,  ALFXR.  T.  JOHNSON, 

Town  Superintendent  &o. 


GOSHFN,  ORA  <GE  Co.,  N.  Y.,  Aug.  21,  1850. 

GKNTJ  : — Having  examined  "StoddarTs  Intellectual  Arithmetic"  pub 
lished  by  you,  we  cheerfully  recommend  it  to  the  favorable  consider*, 
tion  of  Teachers,  as  being  superior  to  anything  of  the  kind  we  have  yet 
fteea  It  has  been  introduced  into  the  schools  ia  this  village,  and  w« 


RECOMMENDATIONS. 

trust  that  by  its  merits  it  will  soon  gain  admission  into  the  Schools  and 
Academies  of  the  State. 

CHAS.  T.  JANSEN,  Town  Superintendent. 

J7H.  THOMPSON,  Teacher. 

iLSraLLREOWEN>™st<*»  «f  *•  Villagr. 
N.  W.  BOOLE,  )  of  Goshen. 


From  the  Journal  of  Education  and    Teachers  Jldvocate,  Albany. 

This  Book  is  an  improvement  on  the  Peztalozian  and  Colburn  plan  of 

teaching,  and  ought  to  be  in  all  the  Elementary  Schools  of  our  country* 

It  treats  practically  of  the  Elementary  Rules,  of  Fractions,  of  Interest, 

Discount,  and  Per  Cemtage,  in  a  way  that  cannot  fail  to  engage  attention. 

WILLIAMSBURGH,  Sept.  2d,  1850. 

GENTS  : — Having  used  Professor  John  F.  Stoddard's  "  Primary  and 
Intellectual  Arithmetics"  in  my  school  for  the  last  twelve  months,  with 
complete  success,  I  take  great  pleasure  in  recommending  them  to  Teach- 
ers,  and  all  others  interested  in  the  educational  improvement  of  Youth, 
ns  the  most  perfect  work  of  the  kind  now  in  use. — And  do  not  hesitate 
to  say  that  pupils  can  by  the  study  of  this  Arithmetic,  make  more  rapid 
progress  in  acquiring  a  thorough  knowledge  of  numbers,  than  by  any 
other  course.  I  challenge  the  Schools  of  the  United  States  to  produce  an 
example  of  greater  proficiency  in  Mental  Arithmetic,  than  my  class  oj 
boys  from  8  to  12  years  of  age  can  furnish.  Hoping  that  so  valuable  an 
addition  to  the  text-books  of  the  present  day  may  soon  be  found  in  all  the 
Schools  of  our  country — 

I  remain  very  respectfully  yours,  &c. 

WILLIAM  H.  BUTLER, 
Principal  of  Public  School,  No.  1,  Williamsburgh,  L.  1. 

TO   THE    PUBLISHERS    OF    "  STODDARD's    MENTAL.    ARITHMETIC." 


M.  R.  BARNARD, 
Principal  of  LancMtafian  School,  and  Town  Sup't.  Ithaca. 
October  3d,  1850 


PHELPS,  N.  Y.,  October  10,  1850. 

This  is  to  certify  that  I  have  examined  "Stoddard's  Mental  Arith- 
jnetic,"  and  am  well  pleased  with  it,  so  much  so,  that  I  havo  introduced 
Into  the  Vienna  Union  School  as  a  text-book. 

LEWIS  PECK,  Principal 


MULTIPLICATION  TABLE. 


_i 

2 
1 
4 

2 
4 
~6 

8 

8 

6 

_? 

4 

5 

6 

7 

8 

9 

10 

11 

8 

1 

12 

10 
15 

12 

14 

16 

18 

20 

22 
33 
44 

18 

21 

24 

27 

30 

12 

16 

20 

24 

28 

32 

36 

40 

5 

10 

15 

20 

25 

30 
36 

35 

40 

45 
54 

50 

55 

— 

6 

7 

9 

12 
14 
16 

18 
21 
24 

24 

30 

42 

48 

60 

70 

Z° 

66 

77 

28 

35 

42 

49 

56 

63 

32 

40 

48 

56 

64 

72 
81 
.90 

18 

27 

36 

45 

54 

63 

72 

10 

20 

30 

40 
44 

50 

60 

70 

80 

100J110 

11 
'~12 

22 

33 

55 

66 

77 

88 

99 

110 

121 

;132 

24 

36J  48 

60  72 

.841  96 

108 

120 

-  "  I 


